Can ground only be dug up/down a certain distance from it's starting position?

Yes. There is a min/max level to each voxel. If you lower it as far as it will go, you'll have to break the voxel with your pickaxe to keep lowering. Keep in mind there is a global max you can raise/lower from the originally generated voxel (8 I think?)

What is your advice for clearing a large area?

Stand in the center of your intended build spot, then basically spin around while spamming LMB in an outward tiering spiral (one rotation close, aim further away, one rotation, etc.). It may take a couple clicks. If the ground doesn't level out, it means you need to either remove a voxel (pickaxe) or add one (raise ground).

Also do keep in mind that the more voxels you alter in an area, the more it is going to affect performance while you're in that area. Unfortunately, there's nothing you can do about that.

In addition, I read that eventually monsters will come to attack your bases. Is this just based on where it is located?

Raids occur after you beat bosses, increasing with difficulty with each boss killed. After you down a boss, the raid for that biome is added to the spawn chance. Which biome your base is in does not effect which raid spawns when the check is made.

I read that building a trench around the area will fix it

This does not "fix" raids, it cheeses them since monsters cannot climb 90 degree slopes or jump across them.

EDIT: Also a feature of the hoe that not many new players realize is Shift+LMB to smooth out terrain, but not attempt to raise/lower it. Per the wiki:

To more effectively level the ground there are two things to keep in mind. Shift-clicking attaches the hoe to the level of ground it is pointed at. When not shift clicked it defaults the hoe to the level of ground the player is standing on.