That would be very bad, if it would be working. It is of course not working. The game is linked with you account and it is not possible to change that.
The ID was earlier your in game name. With your name you will be identified from the servers. The name is not changeable in an easy way. The only way is to contact the support (but they wont change it).
Now it is working with a unique ID (v1.7.6). Means you are able to change your name but not your ID.
This version provides complete support for identifying players through
unique IDs and not by names, so that no matter what a player is called
they will remain banned/whitelisted/oped/etc on servers.
from mojang
The reason why you cannot change your ID is because server owner have a problem to identify you. Means if you are banned from a server, you should be banned and not have a chance to join.
Answer for your edited question:
The functionality on a server is basically the same as on a local game. You actually can not have more "games", but you can have more worlds! On a Server it is exactly the same (if the owner has build it like so). If the server owner has nothing edited and just has a bunch of different maps, you have a "new game/status" on every map. There is nothing limited.
Anyway the chance that there is a server that is build up like that is very low, because everyone wants to keep his items and build just one house and that on just one map. If there are more than one map it is likely a mini game map, pvp, skyland or whatever.
There is no possibility (legal and playable on all "online" servers) in any way to get a new status/"game" on a server by changing anything at your client or on your account.
The only way is to ask the server owner to delete your user data from the server.
Resource packs will only replace the graphics (and presumably sound effects) of the resources they are overriding. Everything else will, in general, default to their vanilla graphics. I have often used an HD vanilla texture pack in a modded environment. The contrast between what is replaced and what is not is not really that big of a deal unless the texture pack is a drastic change from general minecraft appearance.
Best Answer
Kind of.
What you can't do is create new blocks with a custom texture without replacing a vanilla one.
What you can do however is creating block models using custom textures for specific ITEMS and display those with the help of ArmorStands holding them/wearing it on their head. You can make them look like regular blocks and have an almost unlimited amount of them, since every damage value of every item can be used to make it look differently as well as depending on the Unbreaking tag you can double these amounts. So a single diamond hoe can hold over 2000 different models (which would cause a lot of lag though).