Many of your sentences are actually correct!
The first sentence is talking about a habit in the past so you should use either the past simple - Kate rang her mother.. OR used to + infinitive - Kate used to ring her mother ..
The next sentence needs an auxiliary - What time does he usually have dinner? - When you add an auxiliary in the present simple the main verb returns to 1st form.
In the third sentence the expression is 'When I get home ....' present simple for future.
Most of the next sentence is fine - but the last part should read 'he will be ready in an hour' - future simple
'How long were you waiting for me?' I suspect is correct in American English, but in British English we would use the present perfect continuous - 'How long have you been waiting for me?' - It depends on the context which we don't have here. I am assuming that you are talking in the present.
The last sentence should be in the past perfect. 'He was sorry that he had offended us.' The action of offending takes place before the apology but needs the apology.
It is very difficult to give a full explanation to all the sentences but I hope this helps