1). Does the dummy Tusker in the solo game have to adhere to size limitations on the DNA cards when deciding to purchase (in other words, is he limited to DNA cards size 3 or less)? Assuming yes.
Not 3 or less, but DNA cards that include size 3. So if the DNA was for sizes 3-5 (i.e. 3 and above), the Tusker could buy those too. As long as Size 3 is on the DNA, they can buy them and play them. (7.2)
Note that that only applies to the Two tusker buying a DNA and being able to PLAY it. The Two Tusker will also buy, as a last option, the cheapest card on the display and just discard it if it can't play it. (Option 4 in the regular Solo rules, Option 5 in the Paul Harford version.) (19.1.4, 19.2.5) In that case, they could buy DNA with any size requirement.
2). I know M creatures cannot survive in MM biomes. But, can they move through them?
Yes, they can move through them (though their migration range is one less than normal) but can't stay there and survive. (11.1c and 2.4a)