Did the sigma 75-300 dl will work with nikon d300?...i mean the auto focus and matrix focus

The Sigma 70-210 f 1:4,5 is an old model, most likely only to be used in manuals focus mode on your Nikon D5x00 camera.
It also needs to be a Nikon version.
Only the Nikon camera's with the LCD screens on top to the right, like D80, D90, D7x00, D300 and above have a focus motor build in, so old AF lenses can be used in AF modes.

Chuck, sorry for the late response. Last days I had to work through several hundred anonymous questions. Most irrelevant and not complete, so I could not answer most of them, but I had to read them all.
Sigma, does not have a service, where you can download a manual. But the manuals from Nikon, most of the time don't tell anything about how to use the lens.
I found a page with all specs. The link is down here.

I have to guess why you did put the question here in the first place. I think because you have a Nikon camera without a focus motor. Like a D3x00 or the D5x00 or a D40 or D60. (for the x you can add 0 1 2 or 3)
If you have one of these camera's the lens can't be used with auto focus You only can use the lens in manual focus. Most other camera's from Nikon, like D80 D90 D7000 D300 and more expensive, all do have a focus motor and can work with this lens in full automatic focus mode.

50mm F2 8 EX DG Macro

Turn the aperture ring on the lens to its smallest setting (largest f/number) and then forget it's there. You can control the aperture from the camera body, the same way as on lenses without an aperture ring.

That would depend on what you mean by "ok." Assuming you get the lens with a Nikon mount, it will fit onto the D40 and meter properly. However, the D40 lacks an autofocus motor and thus this lens will not autofocus. You can still focus manually.

That particular lens should work on the D40 if it is made for the Nikon mount.
If not, you'd need an adapter to fit it to the Nikon mount. (i.e. if it is a Canon-type lens, you'd need a Canon-to-Nikon lens mount adapter).
You'd probably have fair luck selling it on eBay and buying the right kind of lens for your Nikon.

If those lenses have a Nikon mount then they will fit on the D3000 and D3100. However, the D3000 and D3100 lack a focus motor. If the lens does not have the focus motor then you will not have the autofocus capability. Sigma calls their focus motor the HSM; if the lens does not specify HSM then they do not have the motor.

All after market lenses are specifically designed for a brand of camera. They are for Nikon, Cannon, Minolta etc.. They can not be cross branded just as you could not use a Nikon made lens on a Pentax.

Yes, with caveats. First, bear in mind that this lens has been discontinued by the manufacturer. Second, the lens does not have a built-in focus motor and thus will not autofocus on the D40/D40x/D60/D5000/D3000 models. You also won't get 3D Matrix metering on those models. Everything else will work, and all features should work on other models.

Yes its a HMS lens it will work on most Nikons

Check if the lens is on Manual Focus mode.