You don't really need to buy the TBC expansion if you're leveling one of the original races (Alliance: Human, Night Elf, Dwarf and Gnome; Horde: Orc, Tauren, Troll and Undead) until level 60.

You can buy TBC if you're leveling from 60 to 70 and/or plan to start using a new race (Draenei for Alliance and Blood Elf for Horde).

Yes, you can play WoW without TBC expansion.

Yes, you can upgrade your Trial into the full version by applying online with a credit card. This means you can continue playing your trial character.

If you buy the boxed set, you automatically get free 30 days.

No, the characters you create are tied to the server you are on. Your character on A server won't be available on B, C or D servers. However, there is a way called Paid Transfers which you can move your existing character to another server, within certain conditions. This costs money and has a limit of 6 months per character. Most people prefer to make new characters on another server.

There are several types of servers, broadly they are divided into Normal and PvP servers. PvP server means you are free to kill (or get killed) opposing faction players in contested areas.