To save the game rules you've set up in singleplayer, go to Setup -> Options -> Remember Game Rules.
You can't set gamerules for multiplayer servers like you set them up in singleplayer - instead of using the menu you have to use chat commands. Most of those commands can be found on
this thread.
Alternatively, you could load a mod if one exists - for example, if you want to play Judo, you could type "/set mod judo.tbm" and the settings would be automatically applied.