Yes

No

Somewhat more seriously, the tiles have in order 1 / 5 5 5 4 / 5 5 5 4 4 4 squares starting from the most time efficient cards.

So with 8 7 7 6 time in the seasons you could get 30, 25, 25, 25 squares filled in = 105 total. With 4 monsters, you're up to 121, exactly filling an 11x11 board without the holes/mountains.

I may have got the math wrong, I did it quickly in my head. But it seems reasonable enough.

The board without wastelands has 116 spaces, and with wastelands 109 spaces. So it's probably (pretty surely) theoretically possible to fill both of them with the right luck with the monsters.

If there had been edicts that encourage trying a bit harder someone might get close, but with monsters in play it is unlikely.