The answer depends, I guess, somewhat on the scope of your visit to Chichibu. I.e. do you want to do the 34 temple pilgrimage because of a religious reason and thus absolutely want to visit all of them? Or is it more about sightseeing?
If the second is true, for 34 temples (plus once you are in Chichibu, you will also want to see the famous shrine) in 2 days @ 7 h hardcore sightseeing every day makes 2.5 temples per each single hour, so about 25 min for each temple, including the time you need for transportation, so probably leaving you an average of about 10 min to actually see each temple. Apart from being very hectic, I think all the temples will just mix in your head to one big conglomerate as you don't have time to enjoy the particularities of none of them.
What I would do, is to do the ones farther away (30 - 34) by car, maybe not all of them, just pick 2. The ones in the city (probably not all, but do visit the shrine!) , I would do by foot, and I would also do a few farther away by foot, to enjoy the countryside around. I know, December, but still, unless it is raining/snowing, walking should be enjoyable.
I personally did 25 - 29 by walking, which was very enjoyable and took essentially a day, doing it in a relaxed way. There is a lunch option at temple 28 plus an other very peculiar attraction to visit.
On the previous day I had done 13 - 22 (actually 22 - 13) by walking. While the ones in town are nice to walk to, 20 - 22 were not specially nice to walk to, because of the traffic.
I haven't done 1 - 5, but I have been riding through that valley by bicycle some time ago, and think to remember that traffic there was not so bad, so walking should be enjoyable.
As you have a car, you can drive up to one and then visit a few that are closeby walking.
Here a useful map for the location: https://www.google.com/maps/d/viewer?mid=1FTwG_1aC38rW9olEeOM-CcmnGWA&...
There is also a Chichibu pilgrimage enthusiast on this forum. If you search for previous Q&As about Chichibu, he/she gave further ideas.
Your second question, what to do in the evenings in Chichibu: onsen? dinner? resting for the next day? Probably there are also some bars with Karaoke around town, if that's for you. (Chichibu is not an onsen destination, but after a day out in the cold either walking or driving, some hot soak should be enjoyable and there are at least 2 onsen options available).
Enjoy your trip to Japan!