A trials freewheel should engage almost instantly. Chain slack can produce a little bit of delay and backlash, but not to the degree that you describe. You should probably go ahead and order a spare freewheel to have on hand and definitely tension the chain.
Regarding trackstands, the easiest version (if done properly) is to roll along the side of a mild incline (1 or 2 degrees) and then turn your handlebars as if to begin going up hill as you come to a stop. It doesn't really matter which side your front foot is on, what is important is that you turn your wheel in the uphill direction. The sharper you turn the bars, the easier it is to balance. Don't apply your brakes except to bring the bicycle to a stop. Once stopped, use pressure on your front pedal to hold the bike in place. If you begin to fall toward the incline, apply pressure to the front pedal. This will shift the bike uphill slightly and get it back underneath you. If you begin to fall downhill, ease off of the front pedal slightly, allowing the bike to shift slightly down hill. Practice with your bad foot forward too. The more you do it, the easier it gets and you'll find that you can do it without the incline, with the brakes locked, and without turning your front wheel as much. I still practice it all the time. And it is one of those things you can do indoors when the weather is not suitable for riding (e.g. winter.)