Best time to go is mid/late October. It’ll be warm in the high 20s (low 30s maybe) during the day, but will cool down once the sun goes down. You also need warmer weather because if you pack light, you need to wash your clothes and for them to dry for the next day!
There’s both good and bad about booking booking hotels/hostels in advance. Good, that you know you have somewhere to stay that evening. Bad part is that you are forced to cover that distance on that day, so if you happen be physically unable to make it, you do lose out on your deposit and end up spending money on a place somewhere else. A lot of people doing the round the island bikes normally don’t book in advance because they don’t know how the day will pan out. There’s also no shortage of small hostels along the way, so if they plan a few hours or even half day out, they won’t get stuck with no place to stay.
If you’re not experienced with long distance cycling, you can look into the tour groups that Giant provides. Yes, they can get a bit expensive, but they take care of everything from water and food on your trip. All you need to do is show up. I believe you can hop onto the support car whenever you are over your limit. @okonomiyaki is out on one now and is on a mission for me to report back after his 9 day trip.
As for an electric bike, seems like @Hamletintaiwan and @fenboy got you covered!