actually both are correct.. (that) is optional in some cases... it depend on what is the emphasis you want to put in the phrase and that's it. you are doing just fine! keep it up.

Both would technically be correct but yes, the latter is better cause it isn't lazy English. Although neither of these sentences is a complete, grammatically correct sentence. Only because it lacks the full idea and the finite verb that you'd be performing. I do hope this makes sense and is slightly helpful :)

I'd say the latter. The former is lazy English, whilst people would understand you and the latter is more complete.

Both of these would make sense but I would say that by using 'that' you are making it conditional. So usually 'When I get home and find out THAT they ate my food' would be followed by something like '... I will be very angry'.