Skrulls in the comics used Skrull tech and superhuman DNA to replicate superpowers. The one notable difference is that in the comics, the Skrulls never invaded Earth until they perfected the process. The machine we see in the series is likely off-panel in the comics.

Super Skrull himself can replicate the powers of the fantastic four.

There are other super skrulls who can do this, but not all super skrulls can.

Another is Xa'vin, who could use any of the f4 powers but only one at a time (this may have since changed, they were inexperienced back then).

But other super skrulls have different powers.

Short answer is no. Not counting Chrell, Kl'rt stated once that the Skrulls have attempted to replicate giving the Fantastic 4 powers to a Skrull many times but none of the Skrulls have survived. Only Kl'rt can replicate the F4 powers to a level even beyond the F4 themselves. Veranke also explained the process during Secret Invasion but the procedure in which they acquired their powers was a bit different from Kl'rt's process. Veranke's process involves a lot of phycological/brain stuff in order for the Skrulls to be undetectable by the likes of Professor X and for them to be almost indistinguishable from their counter parts.

No, Xavin can do it as well, pretty formidably even