Hey Csaba,
regarding the questions:
1). Alright, now I think I understand the situation, yet I cannot say anything meaningful without seeing the source code; I will need to ask you for admin login and password for this (you can send the information on my email: support@satoristudio.net).
2). The get_the_terms function returns an array of term objects; please see the first usage example on the official WordPress page I mentioned above on how to use the function.
Sincerely,
Andrii / Satori Studio