Red LED bulbs or strips work in principle, but some/many need additional filtering with e.g. rubylith, or keep intensity/power down by dimming, bouncing the light onto a wall/ceiling or just not installing too many of those bulbs. Of course all the old-skool safelights with (good) filters also still work, but personally I've moved to LEDs several years ago.
Maybe. It's a can of worms you're opening. Frankly, if the original bulb still works, just use that at least for starters. One less variable that can go wrong.
In a true condensor enlarger, a LED bulb for home use in my understanding won't work since it won't focus properly and you'll probably run into uneven coverage issues. In a hybrid diffusor-condensor or pure diffusor enlarger, a LED bulb will work, but use one that goes on and off instantly. Many bulbs for home use have an afterglow and/or start slowly/increase intensity. For enlarger purposes, that can/will be a problem. Again, if the original bulb still works, I'd use that and if you can, order one or two spares online so you're set for the years to come. Enlarger bulbs don't die all that often. Therefore, there's also very little gain to switching to a white LED bulb instead of a true enlarger bulb.
Adofix, yes. Rodinal will be cumbersome and expensive. It'll develop paper alright, but you'll be working at a 1+10 or 1+5 dilution or so and it may not last all that long, and may start to stain at some point. I've done it in a pinch, once, and it sort of worked. But really, don't bother. Just get any decent paper developer. The fix will be OK - fix is fix, for all intents and purposes. Best not use the same bottle of working stock for film and then for paper. Keep separate bottles of working strength for paper and for film. The iodide from the film will slow down fixing paper.
Not to mention the asbestos plate in there that might flake off due to the thing having been thrown around for several decades. I had one of those once, very briefly. It served no purpose and was just a liability to keep around.