'I have yet to.. ' is more formal and would not usually be used in speech, unless you were trying to be extra-formal or posh. To put those sentences into good English. I have to go to the toilet/ I need to go to the toilet. (or to sound like an English person: 'I've got to go to the toilet'/ 'I need the loo.') I don't like him, yet I have to get on with him. To an English person, this sounds wrong anyway, because 'yet' is a formal construction, but 'get on with' is a casual construction. Better would be: Formal = I don't care for him, yet I need to co-operate with him. Informal = I don't like him, but I've got to get on with him.

As a native English speaker, to me ‘I have yet to’ is way more formal than ‘I still have to’, but both are grammatically correct. For your second question; I would say ‘I still haven’t been to the toilet’, and ‘I don’t like him and I have yet to get on with him’. Hope this helps!

i have not to go to the toilet yet,

i still have to do my homework means you may not do your homework and you have to do it .i have yet to do my homework means you do some homework you don't work out it and you do it still.