The insides of diablo 2?

[ShadowHM]

1.) Yes.  You can convert a classic character to a LOD character at any time, but you may not convert a LOD character back to a classic character. 

As far as the SP and MP, there are two different types of MP; closed battle.net (with 4 realms, which are separate worlds from eachother) and open (found after clicking 'Other Multiplayer'), both of which are very different.  In open you can play your single player characters online, whereas in closed you cannot and must create new characters to play just on closed realms.  Although the prospect of playing your single player characters online is appealing there are many downsides to open battle.net.  First, most everyone on open uses hacked items. With hacked items you can become invicible, gain experience at an ungodly rate, and do hundreds of thousands of damage, etc. Open also lacks the polish that closed has, making it more of a novelty experience to play with hacked items than a place to play your single player characters online.  Thus unless playing with hacked items intrests you, you should play on one of the four closed battle.net realms for MP.
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There is on other possibility, with 'open' or 'SP' characters. You can still play them in a multi-player setting via 'TCP/IP' games, without venturing into the wasteland of open battle.net.

This does require that you know other people who have the game, of course. I played for some time with a group of friends via TCP/IP games, before that group started to dwindle in numbers.