Come is an irregular verb. The past tense of come is came. The past participle of come is come.
She used to write this shopping list in squiggles, and then [used to] come back with only half the stuff that she'd gone for.
Both write and come are infinitives here. They are both related to the same verb, used to. The author omitted the second used to to avoid repetition.
She might have forgotten something and [might have] come to fetch it.
Again, the author omitted the second might have to avoid repetition. Both forgotten and come are past participles.
The omission of words that can be understood from the context is called ellipsis. Here are some examples from the site I just linked to:
We went for a walk and [we] took some lovely photographs.
He wrote to [everyone he could think of who might help] and [he] phoned everyone he could think of who might help.
I can remember his face but [I] can’t remember his name.
Do you want to stay in or [do you want to] go out tonight?