DEcevR - when you’re playing a fish and it dives under the front near the pedals, just push either foot all the way forward.
That folds the fins against the bottom of the hull and should prevent most tangles.
I’ve never had a problem with my line getting caught in the drive system while fishing…and only once while trying to land a nice trout on some non-fly fishing gear (sometimes I sin while 'yaking…caught that one while trolling a kastmaster as I was heading up river to set up for the evening hatch…troll with naughty gear, fish with the real thing once I arrive). 
That fish dove under my feet when I tried to net him and I was worried he’d tangle me up.
Now, when I’m fishing, one foot is forward so the fins are out of the way. It’s a trivial adjustment to make to my sitting/fishing position.
I’ve caught fish directly off the side of my 'yak multiple times (within literally a foot or two of the side of it) so I’m not worried about it spooking the fish (and mine is the bright red color).
Vocelli - for really cold weather, you can get a full dry suit or one of those dry tops with two layers at the bottom. One layer goes inside your waders, one layer goes on top…seals it nicely in case you fall over board.
As for stability. I’ve crawled out of my Outback in the middle of a reservior (during a self-rescue lesson that was part of a kayak safety class I took before buying my own yak). The Outback did NOT tip over and I’m 6’1", 240 lbs!
I crawled right back into it on the first try without even getting close to making it tippy.
The others in that class were all using traditional touring kayaks (those long skinny fast ones) and they all repeatedly tipped over trying to get back in. Self rescue is important to know - check your local kayak shops to see if any offer a basic/intro/safety class.
Around here, the local parks require a PFD if you’re on the water. Check your local reqs or just wear one anyways. I don’t like those clunky old orange ones we all had as kids…there are much more comfortable ones that fit like a vest (floatation spread all the way around).
You might need a larger size vest though to cover it (or be cheap like me and use your current one but don’t button it up so it doesn’t matter that it’s too small).
I’m going to try a chest pack soon in place of a traditional fly fishing vest. I think it’ll reduce the bulk a bit and force me to bring fewer distractions. Fanny/hip packs don’t work as well with the sitting position of the Hobies (feet are slightly raised during peddling to keep your center of gravity lower).
Out here (Silicon Valley area), one of the local kayak shops rents a wide variety of models by the hour/day/week and they’re set up right on one of the local reserviors. So, it’s easy to try a bunch of models on the water for an hour at a time.
KFS has some demo days…if there’s any chance you’re close enough to make it to one. If not, maybe some closer shop has something similar? Demo days are pretty common out here and with several kayak shops, that adds up to lots of opportunity to try 'em for free or darned close.