1) Doubtful. Most consumer surge protectors only have MOVs between hot and ground. Better-quality units have protection between hot-neutral, hot-ground, and neutral-ground, so those ones MIGHT be able to divert surges to neutral. Every single suppressor I have for ethernet, RS-232, or twisted pair has a nice #12 ground lead.
2) The computer wasn't destroyed by the lack of ground per se, but had there been a functioning ground it's likely that the surge protector may have had some effect to reduce the harm.
3) Well considering you've already blown up some electronics, clearly there's a
power quality issue at play. Then again, since you don't mention a surge protector on the TV, it's doubtful that ground/no ground would make a difference in the event of a surge. Buy a good power bar that also protects the coax. What would concern me more is the chassis of the TV becoming energized without a ground path. At the very least you could run into some RF interference problems. Same goes for computers too I guess.
4) Well it would be wise to replace all ungrounded receptacles, but of course budget comes into play. I'd do as much as you can. Might I also recommend a whole-house TVSS in the panel?
When the increase lasts three nanoseconds (billionths of a second) or more, it's called a surge. When it only lasts for one or two nanoseconds, it's called a spike.
"Many UL-listed products are also of inferior quality, of course, but you're at least guaranteed that they have some surge protection capabilities and meet a marginal safety standard. Be sure that the product is listed as a transient voltage surge suppressor. This means that it meets the criteria for UL 1449, UL's minimum performance standard for surge suppressors. There are a lot of power strips listed by UL that have no surge protection components at all. They are listed only for their performance as extension cords."