#4
Yes, the 961, twice a day at 6:30 a.m. (which you won't get unless you spend the night in Tiberias) and at 18:30 (when it's dark so you won't see anything). The 962 on Road 6 is much more frequent. The only reason to take the 961 would be if you want one of the intermediate stops. You could of course, if you insist on going via the West Bank, change in Beit She'an as well, but that would be pretty pointless.
I have now looked it up for you and I see there are several direct buses a day from Tzfat to Jerusalem. Since there are no stops between Megiddo Junction and a set-down point on the outskirts of Jerusalem, they clearly go via Road No. 6.
Your desire for West Bank buses will be achieved when you go from Hebron to Jerusalem.
Two options, in no particular order:
(a) Palestinian bus to the Damascus Gate of Jerusalem's Old City, no set timetable;
(b) Egged to the Jerusalem central bus station, timetable on website above.
I don't know the fare on the Palestinian bus except that it's cheaper than Egged, but you will then have to cross Jerusalem from the Old City to the central bus station. Either a ride on the light rail for NIS 6.60 or a 40-minute walk. If you take Egged to Jerusalem you'll arrive in the central bus station which is very convenient since that - by an incredible coincidence - is where the bus to Masada leaves from.