Ben, I'd watch to see if the fertilizer burn continues or if it is already done. If it continues, yes a good flush with clear water would be a good idea before you add more fertilizer. I wouldn't try to change out the soil completely at this stage. It will do the root systems of your plants too much damage.
On the little suckers at the bottom, I think I'd leave them for now only because you've lost a bunch of leaves already and the plant needs leaves making food for recovery right now. Later you can take them off for the purpose of keeping your plants a nice shape. I never remove mine, though. I'm growing mine in Earth Boxes, so they have lots of room to bush out and sprawl.
Yes, it's common for pepper plants to drop some buds at first, especially if the plants are stressed. With mine, it usually takes quite a while for them to ramp up to setting lots of fruit. Often the plant sets one big pepper, and matures that one, then when I pick it the plant says "phew" and starts producing multiple new fruits.
