I've made a lot of videos in my time, but I've never bothered spending any time on photo resloution. If in doubt, just make a very short demo with your pictures in it and then play it back to see how it looks.

The target resolution (dimensions of the video) will depend on where you plan to post it.

Generally you'll want to create your video in the highest resolution practical. Then you can encode or transcode it for your target site.

Other considerations are Wide Screen VS. Standard. These days many folks prefer 16:9 wide screen aspect ratio.

When I post a video on my own site I make it 640x360 (wide screen). When I do it for YouTube I go for 1280x720 (when possible).

If you're shooting live video you camera may dictate the resolution. If you're doing screen captures or PowerPoint videos completely it's up to you.

It does make a difference, first in size, if you think of it this way, (if you have a container and you put a photo in it that is 20MB, then logically the size of your video will increase,) But only by the compression and workflow that you apply to your video, for example if you use an image, that is already compressed, then you are likely to get fuzzy images,

(which is why you often see ugly looking graphics even sometimes on TV commercials)

The format also makes a difference, and the tool your using, for example if your using Final Cut Pro, PNG is the best format, to use and the resolution can play a direct role in how your workflow plays out.

In the end you want crisp clear easy to read, graphics in your video, this applies to subliminal as well as logical thinking, when your creating a video size can be an issue, if you are not careful you can end up with a 1 Gig, video which will be very difficult to upload and play, so there is a fine line between quality and workflow,

Well, I'm using Windows Movie Maker...never heard of Final Cut. I've got some stock images, and I've been playing with the effects all night. I even figured out how to add music which is soooooo cool! Okay, back to work...geez, this stuff is actually quite fun. Not like work at all.

As far as I'm aware, there is no standard resolution for pictures in videos. Obviously, the higher the resolution the better, but generally anything over 72 dpi is fine. If a picture looks too "grainy" when you have it full-screen, then shrink it down and have a smaller picture against a plain background. 9 out of 10 times it will look OK.