Correct, no public transport from about two hours before sunset on Friday until after dark on Saturday, throughout the year. The precise times depend on the season of the year - obviously it's earlier in winter than in summer, although the total number of hours is the same.
October 10, for example, from about 2 p.m. on Friday (meaning buses reach their destination at that time) until about 6:15 p.m. on Saturday.
December 11, around an hour earlier for each.
December can be cold and rainy, but if it does rain it's usually not for more than a couple of days at a time. In October the weather is generally still very warm and pleasant, although a sudden downpour isn't unknown.
Since this year all the religious holidays you have listed fall on Shabbat, the practical implication is that you won't even notice them. In some years they are midweek, which means far more disruption - not only is there no public transport on Shabbat, but there is also no public transport on the midweek holiday, which is enough to drive even the religious absolutely crazy.
Note that "10-11 Oct. Simchat Torah" applies only outside Israel . This isn't the place to explain why. In Israel Simchat Torah is on 9-10 October.
Do you wish to avoid these holidays or want to be in Israel then in the hope of seeing something interesting? Truth is, there won't really be anything to see, except that during the week of Succot there will be a lot of succa booths (temporary huts) in the streets and on balconies of apartment buildings.
There are no religious holidays in December. Hanukka (December 12 to 19 this year) doesn't affect anything except that kids are off school. It is not a major holiday.