1080p is sufficient in terms of resolution, though 2k or better yet 4k is prefered these days, though resolution isn't the only measure of quality. The quality of the color and dynamic range of the camera and the use of a global shutter (or lack there of) can make a big difference on how good the footage looks in a theater environment, depending on what the footage is like. Footage from a cellphone is not going to have the quality of color or the shutter to hold up well in a theater. You'd really want to spend a minimum of probably $1500 or so and preferably at least $4,000 or so on a minimal setup for high quality video.
As far as editing software, After Effects is not an editing package. You would want to use a NLE (non-linear editor) like Premiere to edit the footage. After Effects is useful for things like titling, color grading, stabilization and effects work. Sufficient quality H.264 is ideal. Probably a high data rate All I frame would be ideal, though the exact best option would depend on the playback gear available at the theater.
As far as how to play it at the theater. The majority of theaters are rapidly going digital. It is easier to manage digital cinema since there are only large files to deal with that can be delivered electronically and don't wear out. Also, the editing is generally done digitally anyway, so there isn't quality loss that would be necessary to move back to film.
320kbps is low for editing sound, but fine in terms of final output. Ideally you would want to record 96khz, 24bit PCM audio for each channel and then do your edits on that and only compress it for the final output.
The bigger deal is that technique and skill make a far bigger difference when blowing it up a lot. A little bit of vibration that isn't that bad on a TV screen quickly becomes physically nauseating when blown up to an entire wall. You need to use good tripods and dollies and such when shooting for the theater. It would likely be possible for a really skilled individual to make something passable with a cellphone camera if the rough quality made sense for the piece, but without proper shooting technique and stabilization (physical, not added in post production) the footage would make people ill to watch in a theater.