Yes, your grammar is fine. The logic of your first example is a little out - if you said it was cold until Sunday, that implies that it warmed up after Sunday, and your reader would wonder what happened between Sunday and today. Perhaps 'It was cold until last Sunday but it has been very warm since'. I think your second example would be a bit more natural with 'was' rather than 'is'.

Yes, you can certainly use 'until' before a past time. 'I didn't know what italki is until last May' should be: 'I didn't know what italki was until last May'.