I recently had an acrylic nail put on my index finger, as I had worn the real nail down pretty far and was (fortunately) playing too often for it to grow back naturally. I was wearing to down faster than it'd grow. The nail I have now is a LITTLE longer than I'd usually have it, but not a whole lot and it's certainly not longer than my other nails, which I keep short. I lucked out on my first visit, as the technician had done nails for a guitarist and put on another layer of acrylic for me, so it's super strong.
Might be a solution for you.
As for strumming, I've recently figured out a good exercise that seems to work (it's kinda what I did when I was learning, but WAY better structured!).
Make a thumbs-up with your right hand (a loose fist with your thumb up) and turn it in towards you, so the thumb is pointing to the left.
Now, whenever you're listening to music, tap your leg with the thumb. Just beat out time with it. Keep it simple.
As you get used to this motion, let your index finger open up a bit, nice and relaxed, and strum your leg, still tapping with the thumb.
See how it's the same motion as strumming? Just keep that up and you'll get it in no time.
Welcome to the forums, by the way. Do look around. There are a grajillion threads with answers to almost any question... and if there isn't, ask, and there will be!