Right now with the spawn "supposedly" being in full swing, they wouldn't necessarily be grouped up ... males would be close to the bank and females would be out a ways from the bank and making periodic moves to the banks to drop a few eggs. Now with the colder than normal weather, rising/falling water levels, and such .... that's kinda been thrown a curve. That seems to have made the fish a lot more finicky than normal. I've even heard reports that Crappie, that should be setting up to spawn, have in fact moved out into deep water and just "hanging out". I guess they're trying to make up their mind about whether or not the conditions are gonna get favorable enough to have a viable spawn.
To answer some of your questions ... yes, getting too close, anchoring, or hanging up and disturbing the brush "can" spook the fish. Sometimes even just catching one can turn off the rest of the fish on the same piece of cover ... and they may move deeper into the cover, or simply just swim away.
On a fallen tree (laydown/deadfall) the last thing you want to do is get over top of it. It's usually best to get out from the top and cast towards it, working the water column from shallow to deep on successive casts. Using a weedless jighead will allow you to bump the jig over any branches it comes across.
When the spawn is over and the fish have had a chance to recoup and school back up again, standing & fallen trees can be a magnet to these fish ... especially on banks that have shade out over the water they're in for the first part of the day. The bigger the tree and the more big branches it has, the more likelihood that some fish will be hanging around it. The farther out and down into the depths the better, also, as that gives them shade in several forms (shade from the live trees along the bank, shade from the big trunk & branches, and shade from depth).
That's just some of my experiences, so hopefully others will chime in with their own ideas !!
And to Crappie.com !!