By theory, no. Just because the phones might run the same O.S. doesn't mean that there is a good chance they'll both run the same video files. Though as more time goes on, most phones will have enough power to do it. So then, by theory they would. The next video files on the horizon that will be a ways out is seeing phones play 1080P(a lot don't even play 720P yet, but the one that do, share O.S. with ones that don't).
The phones can have the same O.S., but one might have a much better cpu, gpu and can handle the needs of h.264 or HD 720P even.
I see you have an Eris listed. The spec on the phone say it can play Video: MPEG4, H.263, H.264, WMV. So that's good, but it might not like the spec the video's you have been encoded with. Too high a bitrate, VBR, audio codec etc. The Evo is close to twice as powerful as the Eris as well.
Yes, you can drag and drop the video files as you would for music as well.
You should list your full specs that your videos have been encoded with and what software you were using as well. Handbrake(software)?