Can I jumpstart my car if the alternator is dead?

Depends on the car. On pretty much any newer vehicle probably not. It's possible though. Really all the alternator does is charge the battery, and the battery is mainly needed to start the engine, once the engine is started the alternator and battery aren't necessary for the engine to keep running. But newer vehicles are a lot more picky in regards to electronics, so no guarantee it will work. I know I once drove my '68 VW Beetle with a dead alternator for about 3 months, just roll started it every morning and afternoon(manual transmission, get the car rolling and pop the clutch and it starts). Of course being an older car it doesn't have the electronics drain new cars do so it worked just fine, but on a newer car running your car this way isn't ideal and you won't have the extra power to continually use all your electronics(radio/lights/air conditioning/heat/wipers/etc) but the engine will run and you can make it home. Now if the pulley on the alternator is locked up then you definitely don't want to run it until you replace the alternator.

Yes but you can't drive it like that. If the alternator is dead you will be doing serious damage to your car by trying to drive it. It will die again very soon. The alternator provides power to the spark plugs so they can ignite fuel. Without an alternator, the spark plugs won't spark and you will misfire and stall. I would definitely not suggest this.. just get it towed, unfortunately.

Need to swap in a fully charged battery to possibly start it (depends on how the alternator fried). The engine can run for a few minutes (sometimes longer, say an hour with no lights, no radio, no fan, etc) off the battery alone.

When jumping leave the cables connected 10 minutes or longer to charge your battery before you jump it. When you disconnect you don't have very long to get where you are going.

You can but it will die the moment you break the connection with the jumping vehicle.

You can, but the engine will die as soon as the cables are removed.