Sigma - 30mm 1.4 DC DN Contemporary Lens for select Sony APS-C E-mount cameras - Black

Yes it is compatible with a6000 great lens so far

Yes!

I I’m not a sports photographer but I think it would work well

Yes, you can put this e-mount on an full-frame e-mount (FE) camera body...but you wouldn't really want to. There is going to be a significant vignette factor at all the corners. And you can tell A7-series bodies to crop down for a lens meant for an APSC-sized sensor...but why? It is best to stick to an e-mount for Sony 6x00 series and an FE lens for the A7 bodies.

Yes, this is a perfect lens for your Sony, says this owner of an a6300. The hardest choice is choosing between this and the Sony 35mm f1.8. For photo-primarily shooters I would suggest this excellent Sigma (rated the #2 in sharpness for the e-mount system, second only to the newer Sigma 16mm f1.4 wide angle lens for e-mount). There are lots of discussions about this lens on YouTube. There were once some focus-lag issues at its release, but this has been fixed with a firmware release. For photo+video users, the slight nod goes to the Sony, which lets in a little less light and is not quite as sharp, but DOES have image-stabilization that is handy for your video. The cost differential favors the Sigma and varies between $60 and $110, depending on whether or not Sony is offering rebates (this summer Sony has offered $50 rebates on the 35mm in May/June and now August). One final nod to the more expensive Sony: it is over an inch shorter, thus making it nice for walkabout, all-purpose use. It really is a tough call... But by all means this is a great lens for your Sony a6300.