First of all, welcome to the UltraMixer community.
Yes, you easily activate your licence on your new computer. The only licencing restriction is you are not allowed to use UltraMixer on more than one system simultaneously.
Registered user of UltraMixer can update for free up to UltraMixer 2.5. After that you can upgrade to UltraMixer 3.0 for example for a special upgrade price.