In a commercial website under wordpress, can I use a wordpress plugin under GPLv2 ?
Yep. Note that we're now up to GPLv3 and other variations. There are certain types of limitation to the so-called "copyleft" license, but they don't bear on the "normal" type of usage you're referring to. The Wikipedia entry looked pretty good to me, if you want details.
If a theme is under GPLv2 can I use it for a commercial client ?
I see that often plugins have a pro version, do I have to buy it?, Or can I
just use the free version?
You only have to buy the pro version if you want whatever is available in or in relation to buying the pro version (like enhanced support or customization services or other offers). If the free version (at least the free version under whichever GPL from the WordPress Plugin Repository) suits you, then you can run with it.