So I've been trying to figure out how to tell how many beavers are in a typical colony like when you find a spot how do you know roughly how many beavers are actually there if there's multiple lodges , bank dens, dams or just a single bank den, chewed trees, amount of chew sticks

Also how far do kits normally travle I try to avoid catching them best I can by staying away from dens but still seem to catch them is there any way to avoid that or is it just the way it is

And how does water levels effect beaver movement if your trapping in a creek and there calling for rain

When rain and rising water come beaver are on the move. Time to have all your sets ready.

Avg colony where I am is around 6-8 beaver;
A new colony will have two then the next year 6 then next year 10,plus or minus a couple on average.
The most I have taken out of one colony was 21 beaver.
Small beaver will travel just as far as adult beaver.

I got 18 beaver off of one lodge last year or in that 100 yd stretch. On the opposite side of that island, 100 yds as the crow fly's we got several more. This year I got 8 off of one hut. I'm sure there's more. I'll be back to get them after ice out.

State of the lodge and the amount of cuttings you see are a good tell. A bachelor beaver doesn't upkeep his house at all. Looks like a pile of sticks on the bank. No mud. Pair with no kits you wont see a lot of cuttings or big feed piles.Well maintained hut/dam, likely have a full family and a good sized feed pile.