The router converts the pointers approaching over your Internet connection into a wireless broadcast, sort of like a cordless phone groundwork station. Newer DSL and twisted cord modems come with integrated wireless networking capability and are called modem routers. If you do need to buy a wireless router, be certain that you buy a wireless router and not a wireless access issue.
Since I've had my unit, I encountered issues with connections using the standard WAP security, and even in some cases the WAP2. In general though, I've always setup MAC addresses in the Device Allowed List as there are fewer units that I connect to on a regular basis. The only drawback (in a sense) is that when using your Hotspot for another unit to connect to your TAB, your unit is seen as a unsecured unit (no lock appearing in list of available devices), but it is secure. Actually better.
Regarding the upgrade and the issue with not seeing Flash. If you do a search on Android & Adobe or Flash, you'll find several write'ups on the transition Adobe is making as well as Android with respects to viewing graphics/video's. There's more detail to read then to retype here, but here's one link that you can start reading up on...
