Lots to cover here. I'll try to give relatively brief answers. Hope they make sense!
1. Occasionally. It varies from projector to projector and source to source. How sensitive you are to it is also a factor.
2. There is a certain amount of display lag with virtually every type of projector available today. As with the above answer it varies from projector to projector, and generally speaking the amount is anywhere from one to several frames of lag. PJ's with pixelworks processors are generally regarded as the ones with the least amount of display lag. Turning off unnecessary image processing usually helps to minimize it.
3. Every projector has a native resolution and scales content accordingly. For gaming the answer is usually to have your gaming system set to the pj's native res.
4. Your mileage will vary with pc's. There are a lot of factors that affect this, from panel misconvergence to the quality of the optics in your projector. I use a pc with my projector and it's plenty good enough for me, but text is certainly less sharp than on my lcd monitor. Of course, we're also talking the difference between 19" and 92".
5. Viewing angle is going to be affected most by the gain of your screen. Higher gain will make the image brighter in the prime seating position but limit off axis viewing somewhat. Lower gain screens are pretty good for dispersed seating arrangements.
6. Some still have loud fans. Usually more of an issue in DLP PJ's than LCD PJ's, but there are exceptions to the rule. This can also be affected by what lamp mode you run in and your altitude.
7. Don't even remotely expect 30,000 hours from a lamp in today's mainstream projectors (I'm ignoring the newer LED tech just starting to enter the market). Most lamps are rated for 2000 - 4000 hours depending on lamp mode though many pop significantly earlier. I've seen lamps go in as little as 10 hours (obviously faulty) and I've seen one still going after approx 5000 hours. The bulb will also dim over it's lifespan, the most of which usually occurs within the first couple hundred hours.
8. Not in the way you probably are thinking of burn in as with phosphor based displays i.e. crt and plasma. You can have burnt polarizers on LCD pj's, etc.
Hope this helps a bit, and good luck!