Yes you can revisit with a Eurail Pass a City as much you like :)
Note that the Eurail Pass can´t open the gates at the station and you just have to show your pass to the staff at the gate that then open it for you. These gates are only on major Stations and atleast one of them is always staffed.

Just note that the 22days is a consecutive pass means. If you start your first journey you have consecutive days of Travel. As you wanna go for weekend trips it´s maybe better to use a Eurail Global Flexpass like 10days in 2moths then you can decide in a period of 2 Months on which days you wanna use one of the 10Traveldays.

Maybe @Superalbs  have some suggestions for trips out of Liverpool.

Ow, I thought it would be 22 days any time, until 11 months. But ok!

Thank you for answer! :)

@Pamoliveira 

the 22days is a consecutive pass means after purchase you can select within 11months when the 22days period of validity starts.

The Flexipasses for example 10 or 15days in 2months or 5/7days in a month can be used like you thought but just in the period mentioned for the pass.
The validity period of 1 or 2 months muss be selected within 11months after purchase

For SHORT trips around just Lṕl there are local cheaper tickets: google mersey travel. You will need a local chipcard for that.

In the UK there are also a lot of what they call Rover or Ranger: 1 or multi day tickets for train travel (as much as you like or can do), off peak, for smaller areas. Just use google to find endless lists.

But if you want to make many longer train trips on InterCity trains, the you cannot beat EUrail-UK fares are sky high!

You could of course also buy 2 ´10 days in 2 month´ passes for mor weekend trips.