Being an Italian native speaker, I sometimes write ate when I should have written hate, and vice versa.
Is there a mnemonic I could use to remember when I should write ate, and when hate?
There isn't a well known mnemonic, I think because it's not usually a cause of confusion to native listeners. To help, I'd suggest the following:
ate is an anagram of eat
hate is tattooed on the fingers of one fist, love is tattooed on the other (if you're a biker, seaman, etc).
These are self-composed mnemonics.
When hate hated itself, it ate the h.
I hate pronouncing h, so I ate it.
Well, try to think of "ate" as "hate" with the "H" eaten.