Hi,

I was wondering if it's okay to use different tires (brands) for front and rear?

Depends.
In a pinch=yes
short term=yes
same size=yes
same performance category=yes

Any no's, then I'd say not.
I used my 16" spare when I had to swap out one o my 17" wheels, and I really could not tell a difference. However, I did not "test" the car in this condition. and it was only for a couple of weeks.

Thank you.

What do you think about front Bridgestone S-02 & rear Kumho MX?

Pretty good mix. But keep in mind my first response. You should be fine.