What kind of screws for crawl space vents

I would probably use some rigid foam insulation (2 or 3" is probably good, it's generally rated at R7 per inch - and you can stack it, it doesn't have to be a solid piece), and then use spray foam to seal it up around the edges and hold it in place.

It looks like a metal sill all the way around, so that's going to cause a lot of heat transfer anyways - ideally, to make it as warm as possible, get rid of the metal. You can also then pull off the trim and just put some backing in, and a piece of drywall (or plaster) to finish up the inside.

The most important part is making sure it's sealed to the elements from the outside, like rain/snow. You don't want water coming in and getting into your walls. Depending on the outside condition, get rid of the louvres. Ideally you would put a piece of plywood in place and then if you have siding on the rest of your house, put siding over that as well. You might also be able to just leave the lovres there, but seal them up (with caulking outside, spray foam inside) so they don't open and don't let anything in.

The vent flaps are easy to open (by design, it has to open with air pressure) so birds and rodents could easily open them up and make a home. Birds are relatively easy to evict, but rodents are likely to chew their way through the duct and find their way into other places. As for the crawl space vent, I wouldn't want a possible intake vent so close to to the dryer exhaust, it's a humidity issue waiting to happen. So because of that, I'd go for the roof vent. Try to clean it out yearly, and make sure to clean the lint trap out of the dryer between each usage.