Idioms – Is It Acceptable to Say ‘Fix Somebody’?

As Jim points out, the ordinary way of saying this employs not+infinitive, just as your first example would if it were negated:

I would rather not read a book.
I would rather not have gone to the party.

When you employ a finite verb in the second clause you have to supply a subject for it, even if it is the same subject as that of the main clause:

I would rather he hadn’t gone to the party.
I would rather I hadn’t gone to the party.

She would rather it weren’t so cold.
She would rather she weren’t so cold.

But versions with repeated subjects may sound odd to some people, particularly in conversation.

In any case, the rather constructions really express preference rather than regret. I suggest you avoid rather, and stick with wish in these situations.

"The team has yet to win a game" means that, as of this time, the team has not won any games. Depending on the context, it could mean that they have never won a game since the team was first established, or it could mean they have not won any games in this season or this match.

If you are trying to describe a situation where the team must win two games to advance to the next round or something of that sort, and they have only won one so far, you could add additional qualifiers to the sentence to narrow the meaning. Like, "The team has yet to win a game in the second round" or "The team has yet to win a second game".