With the exception of the helmet point (which could potentially be grouped with banners given that their specific use was identical to that of banners), all of these ideas are centrally focused on the creation and use of banners. Unless the mods want to get really technical regarding helmet decoration, I don't think this qualifies as a wishlist.
That said, #1 would be really awesome but I'm not sure if that would be possible logistically from within the game since we have to store the final patterns somewhere...since this would most certainly indicate the use of something like a skin server, it would be most interesting to see Minecraft be updated in such a way as to allow the use of traditionally out-of-game tools from within the game rather than having Minecraft simply point us to the links. There have been mods that allow the user to play videos and browse the internet within Minecraft, so I can't imagine this concept would be too far-fetched on at least an OOC basis (ie, something handled within the main menu/pause menu, like video settings or game controls). I guess the obvious question would then be what would display when this server becomes unavailable?
#2 I thought was basically already in-game. You can place a banner freestanding and it will hang from a little pole, and if you hang it on a wall then the pole is transfigured into a horizontal bar for it to hang from. Perhaps the size of the freestanding/held banner could be enlarged so that it gets displayed a bit more prominently, but I guess the easiest fix (assuming this is not already the case) is to allow the banner to be crafted onto a headpiece similar to the pillager implementation. In modded, some mods allow you to add modifiers to items by crafting them together and then when you want to take off those modifiers you place the item back in the crafting grid (the result of that craft gives you a modifier item back and the original item is reinserted into the grid). Similar implementation could perhaps be applied here to put on/take off banners, but that is assuming it won't conflict with existing NBT structure.
#3 eh, probably too much detail for too small of an area. Needs an illustration, I think. At any rate, probably could be folded into the considerations for #1.
#4 is probably a case of "hadn't thought of that!" or "haven't gotten around to it yet". Beds were changed to be tile entities recently, which allowed them to be dyed. Shields are entities (dunno if they're considered tile entities since they can't be placed in the world), and can be crafted together with banners. Seems like we should be able to craft beds with banners in the same fashion.
#5 is similarly implemented for shields, and while I don't oppose the idea being applied to chestplates I just don't think there's enough real estate on the chestplate model for a banner to be applied without looking weird or just plain awful. Perhaps you could manage some mockups to illustrate or come up with a specialized subset of rules that limit this to simpler designs that would probably fit?
#6 yes please. I like that Mojang thought a little bit out of the box and applied banners to pillager heads, but to me that feels a little bit like a hack--much like the use of a punch bow to gain unlimited flight with elytra.
I would be inclined to consider each of the OP's points to be closely related to the root idea of adding more/more customizable heraldic display options.
Has roman standards
The image (of a vexillium is at https://goo.gl/images/N2hqJT ). Adding finials (eg the eagles found on the banners of roman legions) would be a visual enhancement, but would seem to require giving the banner some of the functionality of the armor stand and might require splitting banners into pole- and wall-banners.
Neither is [IMO] a 'deal-breaker', however:
If the current banner continued as it is, but the armor stand was expanded to allow display of a banner in place of everything from the "neck down", pumpkins/JoLs/current helms and heads would all be available as finial elements (as well as all the current blocks – with the help of pistons and provided one did not wish to move the display).
1. Make a UI where you can paint your own banner patterns that are completely custom.
As mentioned by DuhDerp, the technical requirements of allowing the patterns to be universally displayed may be prohibitive.
Server software could be modified to allow the uploading of patterns, avoiding the need for a central registry as is done with skins.
Alternately, banners could be allowed to display maps (which have been used as a kluge/work-around to create custom art from within the game).
2. Make it so Banners can be on portable flag poles. Eg. Like Roman standards in battle
This seems to largely reiterate the  point.
Allowing a non-banner-bearing pole extension under and as a part of banners (rather than placing the atop iron bars or the like) might address what the OP is requesting.
3. Make Horses have coat in banner patterns, like the Medieval Knights did.
Banner patterned caparisons [formal term for an heraldic or otherwise decorative horse covering] would be a nice visual addition (and were often worn over barding with a secondary function of helping to keep the barding from the weather).
This would, however, mean that horses were being equiped with a tile entity (in addition to saddle/armor), however donkeys/mules and llamas can already be equiped with chests so this should prove possible.
4. Make custom bed covers with banner patterns.
Another visually nice idea (although lowest on my priority list of those posted), but – considering banners can be applied to shields and both are effectively static displays – this shouldn't be too difficult.
5. Make chestplates be able to have banner patterns, like the medieval knights displayed their coat of arms of them.
Rather than altering the chestplate (which tends to vanish late-game in favor of elytra), I'd rather see the addition of a tabard or surcoat item.
RE DuhDerp's comment about more complex patterns not looking well when displayed in this manner:
This was actually a 'thing' IRL (particularly with later and heavily "quartered" arms). IRL the solution (until arms became almost entirely ceremonial) was to wear a simplfied version (usually accomplished by removing small elements that did not actually consitute part of the formal blazon). Within MC, I'd rather have the ability to put any banner on a tabard and leave it to individual players to decide whether or not a particular design 'worked'.
6. Be able to make Plumes on helmets using feathers and dyes
Feather could certainly stand a new use (even a purely cosmetic one)
This would somewhat complicate helms (for both data storage and display), but the number of plumed helms in a world is likely to be 'small' particularly as not all players are likely to avail themselves of the opportunity.
Assuming tabards/surcoats were added, I'd be willing to forgo plumes in the name of simplicity, but no objection otherwise.
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WARNING: I have an extemely "grindy" playstyle; YMMV — if this doesn't seem fun to you, mine what you can from it & bin the rest.
Yeah, I know it's a thing in real life. What I was saying is that the chestplate model might not have enough pixel space to shrink down a banner-sized pattern well enough to allow it to fit properly...it would either "scrunch" too much due to a lack of resolution or it just plain wouldn't have enough space and you'd only see a portion of the pattern.
Banner designs should only be able to be added to tunics instead of chestplates.
Are metals dyeable? I'm assuming not, in which case I totally agree with you. It's kind of a shame though, since you can't wear banners on your head like illagers do when you want armour that stands an actual chance. That should be a thing too!
1. Make a UI where you can paint your own banner patterns that are completely custom. Paint them? Like using a Canvas?
2. Make it so Banners can be on portable flag poles. Eg. Like Roman standards in battle Are you able to place down the Flag Poles? I think you mean like carrying though, in which case banners are already carried? You probably understand more then i do. Would be cool if they were liek flags, and you could putthem on horse saddles.
3. Make Horses have coat in banner patterns, like the Medieval Knights did. Like on the Saddle? Like a skin?
4. Make custom bed covers with banner patterns. Agreed.
5. Make chestplates be able to have banner patterns, like the medieval knights displayed their coat of arms of them. Like the knights, that would be really cool on Chain Mail, maybe even medeival armour aswell.
6. Be able to make Plumes on helmets using feathers and dyes I like this one, like special helmets and hats. I don't think the knights did that, but the Indiginous groups of the US and Canada did.
My responses are in Bold. Although it may have seen so, I'm not being mean and actually like your ideas. There rather cool, and would fit well in the game, I would use them often. Support!
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Hey guys I'm James, I used to be a noob but now I'm not, I finally figured out how to use TextCraft so here's a banner for one of my suggestions.