To be clear,, parallax adj is not focus adj. It's to complected for me to explain, but you should be able to adjust focus with a ring around the objective bell of the scope, while the parallax adjustment is often on the side of the scope. Most hunting scopes are fixed 100yd parallax. Pistol, shotgun, & 22lr are fixed 50yd parallax
One of the problems I found with zoom at short ranges is the angel of view. Where 4x @ 100 yds may be 15-20ft, at 20ft distance it may be down to 1-2 ft of view. So, clarity becomes secondary to being able to get the X on the target.
I ran into this with my .22 BSA Lightening. I mounted a SIMMONS 44 MAG. 6.5X 20 A/O MIL-DOT. Target shooting at 30ft I get something like 5inch field @ 20x. That's fine for paper, but a bird or squirrel, never.
Granted, 20x is a bit much for close work, but it allows 1/2 inch groups, on a 1.5 inch target(see attached)..
For me and my low speed style, a good red-dat for near and the 4x or 6x for normal hunting..
If you can't get the scope with good parallax adj. Look at a scope that has the base parallax set to 50yds.
As far as focusing. a scope will have it or not..
My $00.0002