Olympus E-510 70-300zukio

Most camera's can't focus when the aperture number is above 5,6. Although your tele zoom starts at 4,8, it reaches the 5,6 at about 150 mm. So from there and up it can't auto focus. You still should be able to focus manually, but for wild life or sports pictures, it is useless.

No, but it appears that there is a bad tooth or something in the gear mechanism of the lens. Internal issue, hopefully over time it will "go away." Cross fingers and hope it does not get any worse. I would carefully shake the heck out of it to possibly dislodge what ever it is.

Only if the lens mount is for the Olympus

The lens is definitely faulty. Either return it to the retailer for an exchange/refund or send it to the manufacturer for a warranty repair. Of the options available, a warranty repair should be your absolute last choice.

Yes, no problem at all. The lens is a Four-Thirds mount and that's what your camera is designed to accept.

Please take a moment to rate my reply and feel free to add a comment if there's anything in my answer which has left you with any further questions.

Quick temperature changes may cause this. I have the same lens. May be you must clean the pins while attaching lens to the body. If this information will help you please give your vote. Good Luck.

Haha!!
Maybe its something you're not doing, LOL.
Look on the side of the lens. Most of the 70-300 macros have a slide switch. My Tamron, for instance, needs to be zoomed out to 300, then slide the switch to Macro and its ok. Look for the slide switch. You might also notice lines of a different color to denote Macro.
Some days it too tough to be smarter than the lens,
LOL.

Solved

I spoke to our local J&A Camera shop who gave me a short tuition on the lens.
Most of this I was aware of.
Thank you to J&A and yourselves.
Malc

Focal Lengths for the C-2000/C2020 Zoom Adapter CLA-1 Step-Up Ring F/L+1 +1.6X +2X 2.5X B-Macro Yes Yes (43-55mm not incl. w/lens) N/A N/A N/A N/A B-28 Yes Yes (43-55mm incl. w/lens) 29mm N/A N/A N/A 1.45x 150mm Yes Yes (43-46mm incl. w/lens) 150mm 245mm 300mm 375mm