Thanks for being clear about the situation and giving us some background. I read all of it with interest!
As a songwriter myself, let me first say that you dont try for originals. You sit down and painstakingly hammer the thing out until its done. Sometimes it takes weeks before you come up with all the right parts and lyrics. Sometimes you can nail it in a couple of hours. It depends on the piece, the headspace youre in, and a whole bunch of other factors. I do all that work outside of full band practices so that when were in the studio, the band is working on a more or less complete structure and the rest of the members can then provide their input. There are also some bands who compose entirely through improvisation. My bf, who is our bassist, is also in another original band and thats how they write. Someone (usually their guitarist) comes up with a riff and off they go, which never ceases to amaze me. They will stop to discuss ideas for changes and structure, but Ive seen them come up with a fairly complete tune in a short space of time. But then, were all experienced musicians who have had the time to learn what works best for each of us, and I dont write that way, myself. I need to be alone to do my best work. Our guitarist and I co-write all the material for our band and we do it on our own time, by making simple recordings of ideas and emailing back and forth with each other. The bottom line with writing is, whatever your process, you have to make the time to do it on a regular basis. Song ideas very rarely come out of thin air. Through trial and error, through the sheer doing of it, you will find what works best for you.
It definitely sounds to me that you have the drive, organization and focus needed to lead your band. But you cant force people to do anything. They have to want to do it in the first place. And the guitarist does not sound like he really wants to, or hed be doing it already. Maybe hes not ready to be in a band just yet. As for his refusal to play in 4/4, I agree that thats ridiculous. Some tunes just need to be 4/4 and trying to impose alternate timing just for the sake of it is absurd. There is absolutely nothing wrong with being simple when it comes to song writing. Sometimes, a simpler approach can be extremely effective.
I would suggest picking some really easy, fun, three or four chord covers that you enjoy, just so you guys can rock out and get used to playing together and listening to each other while playing. It can take time to gel as a band, even for experienced musicians. So dont make it too hard for yourselves to begin with. You can always expand your song list to include more complex stuff as you go. Devote part of your practice time to covers and part of it to original development at every practice. And if the problems with your guitarist dont improve under the new practice structure, try putting up some notices at school and see if theres someone else who might be a better fit. You can try posting notices to find a drummer, too. You never know whos been working away on their instrument at home all this time and is now ready to start playing in a group situation. The suggestion of a drum machine or programmable software is a good one, too. We used that before we found a drummer and it worked just fine while we were developing our material.
As a last thought, its really, really important to record every practice. I cant stress that enough. We recently bought a digital recorder, but before that, we just used a laptop with a mic. Crappy quality, of course, but that didnt matter. It was enough for us to hear ourselves so that we could work on any problem areas. You simply cant always hear everything thats going on when youre playing. Hopefully you can find an inexpensive solution for your band. Best of luck, man!