Salem

First, what is the best material to use for bait?

So far I've only noted that in fresh/river/ shallow water I catch more fish using cooked nuts and daisy petals than any other material.

..
Second, Lobsters?
I have about 20 traps spread along a section of the shore and have used every sort of bait I can think of, but not a single lobster (or tuna or sea bass for that matter) yet.

Lobster could be caught in satly water (ocean). If you are playing on Popham, IDK where can you get salty water source. On Providence the town is on the shore of an ocean.

imho meat cuts are best.

My friend and I have two traps on the river next to our claim, we throw snails in there and we get loads of fish..
Perhaps not "loads" but coming back to four or five is certainly better than one, or.... none. :[
Tuna, Sea Bass and Lobster I have yet to run into.
Lobsters usually eat other dead fish so perhaps try oyster meat, crab meat or maybe even fish skeletons if they can go into the trap, I've yet to make my way to the sea to try this out.

I put anything and everything in there that will fit. I've put sliced meat, steaks, flowers, nuts (cooked and uncooked), leaves...ANYTHING, and I've caught a bunch of fish. I have 3 traps right next to my claim and it got to the point to where I had so much fish I would butcher it right there and then put the filets right back in to the trap.

YMMV....

Fish have spawn points. If your trap is in the right environment but you're still not getting a certain species, it's because there is no spawn for that species there. Try moving the traps around. You also might find you catch certain species at first, but that it changes over time. That is because the spawns also move around a bit so you have to keep moving your traps to try to keep catching what you want.

Is there any indicator for the spawn point of fish?

or do I have to move my traps around random and hope I got it right?

It's not visible, I'm afraid. The fishing mechanic is not great, but we've yet to come up with a better idea.

I like how it works is kind of realistic that you have to move the weirs around but is weird there are fish from salt water and sweet water mixed together in my weirs is unrealistic.

Your water is brackish. Simple explanation.