Hello!
1.) First of all not all temples and shrines have opening hours to begin with. You can visit them any time.
Others have, but USUALLY everything is open on a national holiday (and then often closed the day after).
To make 100% sure just check the website of the temple / shrine etc. you want to visit! ^-^
Yes, department stores and restaurants are opened on national holidays (except around New Years).
Public transportation will also be no problem at all.
Sometimes there will be less buses in local areas than on working days, sometimes there will be actually more. It always depends.
2.) Well, I guess it used to be a good time for autumn leaves, but honestly since last year it's getting later and later. Last year the peak was in the first week of December!! I guess many tourists still expect the leaves to turn red around that time.
There are usually always still hotels available a bit outside of Kyoto (e.g. Otsu) - try to check there!
Travel tip: Mt. Koya in Wakayama Prefecture usually has autumn leaves a bit earlier than the rest of Kansai as it's higher!
3.) Sounds good enough! Japanese people love food gifts, so chocolate is definitely a good idea!
4.) Sorry, no idea. Where did you find the information in the first place anyways? Did it say anything about whether English is spoken or not?
5.) I've never tried to travel through Kyoto using a bicycle, simply because most sights are quite far apart from each other, so usually bus is the way to go (they can get quite crowded, though). I doubt it's dangerous to drive there, but when it's crowded you won't be able to go fast anyways.
Hope that helped!
Let me know if you have any more questions! ^-^