Ollie:
Welcome. I'm glad you've found us. And you certainly have packed a lot into your first post. I can't address it all, but others will certainly jump in to help do so. Here's what I can tell you.
Be very careful on grass; it can conceal a multitude of sins, from sharp objects to the slight changes in contours of the ground underneath, to holes. "Know thy grass" before running on it has been my rule. One of the best things you can do to help make good forefoot/midfoot-running form into muscle memory correctly is run BF on hard surfaces (concrete or tarmac). Doing so will force you to lift and set your feet without skidding on landing or pushing off with your toes or forefoot. If you do it wrong, it hurts; this instant feedback is a great teacher.
The longer you run, particularly when you are new to a forefoot/midfoot landing running style, the sloppier you will get and the more you will fall back into old habits. Perfectly normal, but something to keep your mind very actively aware of as you run longer and/or harder.
Sprinting changes things somewhat from a standard BF run in that you will be extending your stride length more, which can lead more to working the hamstrings. Running distances at pace should primarily work your quads, as you use them to lift and set your feet down gently and accurately. You may also feel a little more pull in your glutes. If you feel calf tightness, you are most likely not relaxing your feet enough or failing to allow your heels to touch down gently after landing on the forefoot/midfoot.
What minimal shoes to use is a good question, but one that I would encourage you to put off until you've spent a few months getting your form molded into muscle memory BF first. Jumping straight to shoes to allow you to go further faster is a recipe for stress fractured metatarsals. I got one early on by going to shoes immediately rather than exercising the patience to learn good form first, and I can't in good conscience recommend it as a desirable learning experience. That said, back to shoes. I like the VFFs (the velcro strap See Ya's are the best current model for me). Lots of our runners like the huarache sandals, but I hate having that single cord between my first and second toes. The five fingers have enough friction with all of the toe pockets to keep my feet from moving around and blistering inside them, unlike any other shoes I've tried. And they offer the widest natural splay distance for my forefoot and toes (I have very wide feet). I used the Bikilas for a long time, but they've stopped making those now; my one beef with the Bikilas was that they were really more shoe than I wanted. Vibram has done well addressing that with the See Ya's, although I don't like the laced version and the heavy lace-through material patch they use on the top of these shoes. It doesn't flex well enough, adds unwanted weight and just does nothing for me.
What podiatrists tend to call overpronation - which is certainly a factor when you're running in large, flat-soled, cushiony shoes - seems to me to be the way our feet naturally fall as part of the shock-absorbing process. Many of us naturally have our feet touch down on the outer edge of the forefoot first, then followed by the rest of the midfoot and then the heel. It's just another impact reduction design process. I can't speak to hallux limitus, as it's outside my experience (that's not bad breath, is it? Wait - that's haliTOSis - they do sound similar), but it certainly could impact your running, as you will certainly be engaging your big toes in the process. It probably depends on the cause of the problem as to how it will behave; it could worsen, it could improve, or it could be irrelevant to your running. Someone with more experience will have to chime in here.
Happy running, and again, welcome to the crew!