It's been a while since I've hosted a lobby, but I believe you first go into multi-player. At the main screen you then invite a friend. You only need one to start a private lobby, you can invite more after. There's an option to create private match, I think it's Y, you should see it at the bottom of the screen. Once the lobby is created you can go through all the screens and create any race you want.
The 50 laps in the rain is cumulative, so you don't have to do it all in one race.
The last to first cheevo is tough. To find a full lobby you have to be on at peak time in one of the popular hoppers, usually A or S, but sometimes C and B are pretty busy too. Getting that particular one in a public lobby is damn near impossible. Personally, I didn't think it worth the effort. Now if you happen to have 24 friends you can invite to a private lobby, your golden! LOL
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