2) What do you do when you have your last two corners oriented correctly but permuted wrong? I know that if that happens with edges you just shoot to both sides but corners have three sides.
From your second sentence I'm assuming you've said oriented and permuted the wrong way round. If the corners need to be twisted, then shoot to any sticker on the corner. Look at the colour of that sticker you shot to. Shoot to that colour on the same sticker. Here's an example:
scramble: y R U2 R' U' R U' R' L' U2 L U L' U L y'
so here, if we're using OP, we need to solve the UBR corner. First, we need to shoot to any sticker on that corner, for example BUR. The BUR sticker is same colour as our R face, so after that we need to shoot to RBU. So we would do:
[R' F: R U' R' U' R U R' F' R U R' U' R' F R]
[R2: R U' R' U' R U R' F' R U R' U' R' F R]
You can repeat this process for more corners if necessary.
You can also learn algs to twist two or more corners at once (e.g. the scramble I posted above and its inverse are easy to learn and very useful), but that's not necessary, unless you want to start getting faster.