I'm playing hardcore mode for the first time. So far, I've spent the first day (it's almost night) building a wooden house from trees in a nearby pine forest. There is also an NPC village within viewing distance of my house. I also have enough materials to make a bed, as there were some sheep nearby. Am I doing OK for the first day? If all goes well, I wouldn't be bothered by zombies or skeletons, but will have a restful night of sleep.
If I move A Nether Portal and relight it, will it still work?
If by work you mean connect to the same one in the Nether, it should if you don't move it too far. The rules governing Nether Gates are far more complicated than I care for, but if I remember correctly, the game connects to a portal within 128 block radius topside. This means that if you don't move it very far (128 blocks) it should still connect without creating a new portal. If you mean will it relight, yes it will. You can always check the wiki for more details (http://www.minecraftwiki.net/wiki/Minecraft_Wiki), or there is a topic on Nether Gate linking in the survival section somewhere.