I thought you did sleeping everyday till 13:00.
This is grammatically incorrect. We usually don't use
do + V-ing.
I thought you used to sleep till 13:00.
This is grammatically correct. However, "used to" here changes the meaning, and I think it doesn't correctly reflect what you want to say here. When you use
used to, you're talking about a habit in the past that is no longer true in the present. (look up how to use
used to for more information)
I thought you slept till 13:00.
This is grammatically correct. However, note that you're using "slept", which means you're talking about the past. If you want to talk about an on-going habit, use the
present simple tense. By using
simple past (slept), you're saying that your friend didn't sleep till 13:00 in the past (only at the time where they said "I do that everyday till 13:00").
I thought you sleep till 13:00.
This would be the correct form of your 3rd example. By using "sleep" (
present simple), you're talking about something your friend does habitually everyday.
I thought you said (that) you sleep till 13:00.
This is another possible response. While the correction before means "I thought it was true that you sleep till 13:00", this version means "I thought you were telling me that. Did you lie?". (It doesn't have to mean "Did you lie?" but can also mean "You're not doing as you said".) This version questions their statement instead of the action of "sleep till 13:00".