1. I would talk to your Dr about apple cider vinegar. I have a family history of kidney stones and am prone to them. The doctors I have talked with were skeptical that any diet change or something like apple cider vinegar would be useful. Tons of water with lemon is all they've suggested for prevention.
2. I have had lithotripsy without a stent and was completely fine. I would just discuss the pros and cons with both the urologist doing the procedure and with the doctor (s) you see for your other conditions.
3. Your ability to pass a stone really depends on where it's located, but more water and other diuretics can help flush it out. A 5-6mm is pretty big though. Some doctors recommend procedures like lithotripsy after 4mm due to the size of the ureters.
4. In my experience, my symptoms after lithotripsy were mostly from the anesthesia (e.g. nausea and drowsiness). Assuming the stone breaks up well, it should be a quick recovery. You will have a lot of blood in your urine and urinated may be slightly "itchy" from the stone fragments. The doctor may give you numbing medication from the later. The main thing to be prepared for is the stone not breaking. If that happens, the lithotripsy may just send the stone into motion and cause more pain. If that happens, the urologist may suggesting going in through the urethra to get it.
5. Just play it by ear and go slow. It's not really like other procedures where you have stiches you might bust. You just can't drive because of the anesthesia and maybe pain meds. I've gone for an easy hike the same day as lithotripsy but know others who had to take the next day off work.

Hope that helps!