The home edition is free. But it does need to be registered every year, which is also free, and - I believe - a method for the vendor to ascertain how many Avast installs are active. Registration is straightforward and (usually) quite fast. The "60 days" is how long you have to register it. If it isn't registered within that time, updates cease.
Regarding the slowdown, we'll need more info. Operating system, RAM and CPU, what other software -especially security software- is installed, and what AV was installed prior to Avast.
Also, was there any history of malware on this computer in the past?
BTW, welcome to the forum.