A potted history is brief, a quick summary. Potted meat is meat, usually not of the highest quality, processed and preserved in a tin. The expression is often used in a derogatory way, as it is in your example.
Let's see... yes, Merriam Webster gives as an example quote under "potted":
briefly and superficially summarized- a dull, pedestrian potted
history — Times Literary Supplement
But, if you were to say, for example, "In the interest of time, I'll just give a potted history of this...", there would be no negative connotation.
This does not correspond to the American "canned", which carries the strong connotation of artificial and stale. "Canned history" would be understood and humorous, but it is not an idiom. In American, "the cliff-notes version" is often used, from a well-known series of booklets for students of brief, condensed summaries of famous texts. This too is often but not always used in some derogatory sense.
The OED's entry for do, under Phrasal Verbs, has an entry to do for —, whose definition 1b is:
colloq. To attend to; esp. to perform household tasks for, esp. as an employee.
They give (among others) a 1997 citation from the Daily Telegraph:
Mrs Simmons has ‘done for’ Mrs Lynton-Smith for 24 years.
In context, it usually refers to light cleaning and housekeeping tasks. As chasly says, it doesn't seem to include live-in servants.
A woman who does might have been called, in earlier times, a charwoman or daily woman.
Best Answer
This refers to having a "double period" of history, or two periods in a row.
When I went to high school in Australia in the '80s a period was typically 40 mins, with 8 per day. Double, and occasionally triple, periods were scheduled to allow for a longer uninterrupted block of teaching time.
The reason for using the phrase "double history" in the context you describe may be nothing to do with history per se. It's more likely used to suggest to the audience that the student in question considers a double period to be an excruciating length of time to have to sit next to your ex-girlfriend.