Polania can use Submerge to move from their home base to the lake to the north.

Yes

Rusviet can use Riverwalk to cross from their home base to the farm to the north.

Yes, with clarifications.

When using Wayfare, it’s possible for your character/mech to transport and drop off resources onto a home base. While those resources are on the home base, you cannot spend them and you will not count them during end-game scoring.

Yes

Yes. There isn’t a river between your mech/character and the lake. Think of it like this: If you walk along the shore of a lake, is there a river between you and the lake? Nope. It’s just land, then water. Same thing in Scythe–rivers are between two land territories, while a lake is adjacent to land territories.

"It’s similar to the upgrade on the Produce action, with a bonus. If you upgrade the Produce action, you get to produce on 3 different territories, right? The Mill does the exact same thing–it’s a third territory for production (or a fourth if you’ve already upgraded the Produce action). In addition to that, if you choose the Mill’s territory as 1 of the 3 territories where you produce, the Mill itself produces as if it is a worker. If you choose to produce on the Mill’s territory (say, a mountain) and you have 1 worker there, the Mill produces 1 metal and the worker produces 1 metal. You could even choose the Mill’s territory if there are no workers there, and the Mill would still produce 1 metal (in that example) as if it were a worker. Here’s where Rodney talks about it in his Watch It Played video. Example: You have 1 worker each on a mountain, farm, and tundra. You also have a Mill on the village. When you select the Produce action, you may choose 2 territories from the mountain, farm, and tundra to produce on. The Mill is on the village, so the village will also produce if you want it to. The Mill itself will act as a worker for production, so it produces 1 worker. If you would had another worker on the village you may also produce 1 worker (though having a worker on the Mill’s territory is not necessary for it the Mill itself to produce)."

Yes

Yes. All printed benefits on your player mat are optional, so you can pay to use a bottom-row action even if it is only to gain the associated coins and/or recruit ongoing benefit.

Depends on the player mat.

You produce workers in the same way that you produce resources, with Village as the terrain type that produces villagers. You first pay the cost to use the Produce action (the revealed cost in red at the top of the action). Then you gain the benefit (produce on 2 different territories–ALL workers on those 2 territories may product). For example, let’s say that you have 3 total workers on the board, which means that there is no exposed Produce cost in red. 2 of those workers are on a Mountain and the other worker is on a village. When you Produce, you pay nothing. Then you gain the benefit: Each of the workers on the mountain produces 1 metal, and the worker on the village produces 1 worker. The action is complete. The worker you produced revealed a cost, so the next time you take the Produce action, you must first pay that cost.

No

No. If you select a unit to move, and you don’t actually move it at least 1 space, it has not moved. If you have speed unlocked or use a Factory move action, you can move forward and backwards and end on the same territory that you started on.

No

No. You may only move 2 different units (or more, if you’ve upgraded the Move action).

No

Nope. On your turn, you choose one section of your player mat, and you can either take the top action, the bottom action, both, or neither. You cannot take the same action more than once.

Place those meeples on the 2 territories adjacent to your home base.