Hi, Michael.
1) I gather that there is no reliable water source above the tram this late in the summer, correct? If there is, where along the trail?
There's water at the Ranger Station in Longs Valley, just past the tram station. This is the last potable water. There is a trickle of water at the pipe in Round Valley, but this water needs to be treated or filtered. Trust me; you want to treat or filter this water.
2) Anything going on (fire, construction, etc) that would make this a bad weekend to hike up there?
I was up there Saturday, and everything was fine. It has been warm lately. I'd bring at least three liters each of water. You're going to get dusty; it's a drought year. The Round Valley area is still green and beautiful even in the drought.
3) Would the restaurant at the tram station be open in the morning to pick up some sandwiches, etc, for the trail? Any breakfast burrito recommendations in Palm Springs or near the turnoff to the tramway?
There's not much at the turnoff to the tram as you come from LA. The tram station has a restaurant up top, but I'm not sure if they offer selections to go. It's more focused on the tourists than the hikers. Maybe someone else has better info on the tram restaurant? As you come from LA, there is a little town called Cabazon. At Hadley's, you can get sandwiches that are really good (but a tad pricey). They also have date milk shakes which I find quite tasty.

There's also an A&W rootbeer in Cabazon for that reward rootbeer float on the way home. I don't know how early Hadley's opens; you'd have to call them. Personally, I'd just bring with me from LA whatever I would need.
4) Anything else a newbie to the area should know?
Well, get an early start. It's far cooler on top than at the base station, but it gets pretty warm in the sun. First tram is at 8:00 on Saturday. Probably the standard sun protection is in order: hat, sunglasses, sun screen. I'd bring 3 - 4 liters each of water. The biggest thing for most people is the altitude, nearly 11,000 feet. If you get dehydrated, which happens more quickly at altitude, you're not in for much fun. It can get windy, so sticking a windbreaker in your pack isn't a bad idea even though it's summer. Completely unnecessary last weekend, but you never know. If you haven't already, I'd get a decent map. The SJ State Park website has a reasonably good one -- with mileages.
http://www.parks.ca.gov/pages/636/files/MtSanJacintoSPmap.pdf You can buy a little brochure with a map on it from the Natural History Assoc. at the upper tram station, but that map is el cheapo and I would't recommend it. The view from the top is stupendous on a clear day. A camera and binoculars are in order if you have them with you.
One word of caution: the summit block of San Jacinto is basically just rock, not a trail. Keep an eye on your surroundings so you can get back to the trail on your descent. The rock isn't especially tricky, but you will need to do a little scrambling to get up to the summit for maybe the last .25 mile (probably less).