Hey Mr. C,
I'm just gonna answer your first question, as it is a big one:
Working on songs cooperatively is always challenge. Everyone brings their own unique experiences and listening habits to the process and that can create some issues.
You will start disagreeing on what to do musically in some spots. That's just gonna happen - but it's also where the real great co-writes begin.
See it like this: If you don't have any fights, you're not pushing each other enough.
Something that happens to me quite often is that a co-writer will suggest something we do. And in my head I'm thinking "This is terrible, it's never gonna work".
But from doing this for years I know that I have my blind spots and I will always try what is suggested. And quite often - if you have a good co-writer that is - it DOES work.
If it doesn't work, there should be someone who gets to call the shots. This is usually the person who started the song (i.e. who had the initial idea for it).
The best thing you can do to avoid constantly running into these big confrontations where you REALLY disagree, even after trying out both ways is finding another songwriter to work with.
You may just be too different in style.
Keep in mind that you may be wrong, too. If both of you are convinced that the other is wrong, ask the rest of the band for their opinion.
Btw. my favorite co-writes happened with songwriters who have a completely different skill set than I do. Often I'll focus on melody and sound, and let them focus on lyrics and harmony.
Just some food for thoughts, feel free to ask for details if anything is unclear