can i make forms where future questions or alternatives depends on the answers in previous questions?

Yes.

You can achieve this using Smart Forms. 

user guide:  -Smart-Forms-Using-Conditional-Logic

You can see in the Condition Wizards the different type of condition logic you can use.

Base on your description, I think this user guide 

-How-to-Populate-Field-with-a-Value-from-another-Field matches the requirement also.

Here is a demo form you can try http://form.jotformpro.com/form/41965390166966?

Hope this help. Let us know if you need further assistance.

Thanks.