To address your main point:
You can monetize, but you need
explicit commercial permissions from the rights-holders, ie contact the company in question and request permissions in writing to monetize (ie utilize their material for commercial purposes). There are some games/publishers that extend this write (some conditionally, some unconditionally), but they are the exception, not the rule. You will often find this information on support pages, ToS/ToU/EULA/etc., "About" pages, etc. ( for minecraft, search for Branding Guidelines - found
here )
As far as the microphone stuff:
- Tip #1. Just start doing it, the 'awkwardness' goes away with practice.
- What to talk about? Hobbies, interests, news, tips/tricks, experiences, etc. Really you can talk about anything, depending on the type of LP you're going for... for example it could be very 'vloggy' like "Far Lands or Bust" where the majority of talk is about Kurt's interests, news, viewer questions, etc. Or you could go the 'infotainment' route like HCBailly's LPs - where he goes into a mix of talking/reacting to the story in front of him, and interjecting with bits of facts about how the game works/strategies/etc. for beating a specific part, very rarely delving into his private life.
- How to fill the gaps? There's times for silence and times for words

- in an LP, you don't have to be talking constantly, but something has to be engaging the viewer nearly constantly - whether it's a cutscene, an action filled moment, or just that silence of "I ran into something frustrating!". The awkward gaps are what are solved with your first part of the question "What to talk about?" - don't be afraid to keep a notepad of 'chat ideas', it will give you something to talk about when you run a blank.
- You have options for recording audio, the best free option is Audacity, and truthfully, for just straight up recording your mic, it works as good as anything else (it's more a hardware issue when it comes to raw recording, only when you get to audio editing does it impact the software you want to choose, which Audacity will still do pretty good at, albeit not as good as some pay software). Some people record audio within fraps/dxtory/bandicam/etc. - this is situational, I personally don't like it in fraps because it doesn't allow for flexible editing, but Dxtory and such can record as a separate stream for your voice and the game audio, making editing easier (well, at least if you use a USB mic... non-USB mic's tend to get lumped in with system audio, which means a lot of fiddly-ness)