It can't run Flash, but I believe you can download apps or jailbreak it if you really need to use Flash.
However, some websites have different iOS versions that are still operable without Flash.
Your iPad will run off your Wi-Fi. However, if you want to run it on 3G or 4G, you will need a plan with either AT&T or Verizon.
Memory depends on the person and what you're using it for.
The iPad 2 has a better processor and more RAM.