2. Who (or what group) within MassDOT determines route numbers and where state routes go?
SM-G900P
Some of the state routes are holdovers from the New England Interstate system, while some are coordinated with other states in the case of multi-state routes. Sometimes, a group of them are kind of clustered together (MA 149-151 are all in the same general area, as are 104-106). The rest: who knows?
Adding to the previous comment. Whatever system Mass. developed for its route numbers collapsed early on when the NE Route system gave way to the US Route system in 1927. Under the NE system 1 and 2 digit numbers were reserved for multistate (longer) routes, while 3 digits were in-state (shorter) routes (with a few exceptions). When that system went away, Mass. started assigning two-digit numbers for its own route system, whatever length they were, in many cases changing from recently assigned 3-digit numbers to 2-digit ones. Looking at route lists from the 1929-1933 maps, for example, MA 102 from Taunton to Weymouth was changed to MA 18 in 1931 (which had been assigned 2 years earlier to a shorter route from Rockland to Hingham). Route 102 then reappeared at the other end of the state in W. Stockbridge. While as previously stated, some effort was made to cluster similar numbered routes in one place (MA 130, 132, and 134 on Cape Cod, MA 104, 105 and 106 in the Taunton area), numbers assigned around them were in very different places, MA 107 is in Revere, for example, MA 131 is in Brimfield, MA 133 is Lowell. There was apparently no thought to placing significance on odd vs. even numbers and geographic direction, thus MA 18 is north-south, but so is MA 27, etc.
IMO the route number system still largely reflects traffic patterns of the 1950s and thus should be modernized, removing outdated or redundant routes. MA 28, for example, still runs from the Cape to the NH border, though no one would use that route between those 2 destinations today. I would restrict that route to Boston northward, use MA 25 for the Cape Cod portion, and remove the concurrencies it has with many routes south of Boston (MA 18, US 6).