lots of questions here and all of them have been answered before - so you might want to do a search.

but, essentially, it depends on what you're modeling. so if you are modeling a character that you intend to animate than it's better to keep it to quads as it will deform better - though having the odd triangle or ngon isn't the end of the world if it's in a place that doesn't matter.

if you're modeling an inanimate object, than keeping everything to quads is not really necessary - tho it really depends on how it renders. the more you model, the more you will get to understand what you can get away with.

as for uvs, without seeing your model and your uv map, it's difficult to say whether you need to lay them out again. essentially your uv map is your model flattened so you can paint on it. a good way to test if you've laid them out correctly is to apply the checkerboard map (or some similar type map) to see if you have any stretching. again, you're not going to get this until you start practising.