I guess each case is a little different, because for me .. spacers didn't hurt at all. I guess it depends on your pain tolerance and where the spacers were placed. The only time I felt them was when I chewed up food. Other than that, I didn't even know they were there. The bracers were the worst part for me. But anyhow, to answer your questions:
1. The spacers didn't hurt at all (for me, at least)
2. Getting the expander installed didn't hurt at all, either. But the glue taste is horrible lol. You'll unfortunately tase it again when you get your braces put on.
3. Again, for me, the expander didn't hurt at all. It just made my mouth feel a little tight for about 15 minutes whenever I turned the key. You also feel a little tension in your nose area.
4. Your speech will be affected, but not horribly. If you do a lot of talking, then you'll end up getting used to it pretty quickly. My first day in it was pretty bad .. I constantly had to repeat myself. But after about the first week, I sounded 95% normal. And now, after a month and a half, my speech is 99% normal (I still can't pronounce words with the "e" sound normally).
5. Yes, there will be a gap between your two front teeth, but it won't be that bad. Your ortho will probably give you a power threader or powerchain to close it up.
6. I have a pretty severe gag reflex as well. When they put the RPE in, I did gag a lot for the rest of the day. But the next day, it got better. And also, your tongue does get used to it being there. I don't even feel it now
Good luck with your treatment! You're lucky to only have to have your RPE in for 3 months. I have to keep mine in for 6 more months (after 1 month of nightly key turns).