I ride a 39t inner ring normally now, and paired to a 26t cog, it's still not low enough as I've discovered for some of the climbs here. Therefore, I personally don't recommend the cost of a new 39t chainring, a 26t cog max cassette, though I believe the 105 derailleur will do a 28t cog.
^ Yes, should fit your 105 BB.
Yes, friction shifting a FD is preferred, IMHO. Fine trim.