I am staying with my parents for two week and then I am visiting my granny.

[Vladv1]

If I have two planned events in the future, is it possible to say "I am staying with my parents for two weeks" and "I am staying with my parents for two weeks and then I am visiting my granny". And could the same two sentences be used with "I am going to stay" instead of the present continuous?

 

[jutfrank]

If I have two planned events in the future, is it possible to say "I am staying with my parents for two weeks" and "I am staying with my parents for two weeks and then I am visiting my granny".

Yes, very good. This is the use of the present continuous to talk about arrangements. It means that you've already arranged this with your parents and granny.

And could the same two sentences be used with "I am going to stay" instead of the present continuous?

No. If you did that, you'd be presenting the actions as intentions instead of arrangements.

 

[emsr2d2]

If I have two planned events in the future, is it possible to say "I am staying with my parents for two weeks" and "I am staying with my parents for two weeks and then I am visiting my granny". And Also, could the same two sentences be used with "I am going to stay" instead of the present continuous?

Note my changes above. Don't try to start sentences with "And". You had two instances of two spaces between words.

Note that "I am staying with my parents for two weeks" doesn't, on its own, express the future. It could be said any time from the day of arrival at your parents' house until the day before you leave.