Can I use Avid olive and connector insert in a Shimano brake?

No you cannot. They are not cross compatible. Shimano Olives, hose and inserts only work with Shimano components. The same is true for Avid brake equipment.

Beyond not being designed to work together you void any warranty claim by not using compatible equipment. You also give up any legal approach to the manufacturer if you use other company's parts. So if you crash because the brakes failed and want to say that's Shimano's fault and it actually was. They will say it had Avid olives and inserts on it.

Yes. Used Shimano specific olive pins on my Avid Elixir 5 and Sram DB5 with no problems at all.... Been using them for about half a year now. Still holding strong. No leaks at all

I have got a lot of shimano pins and olives here and now i switched to sram/avid HRD (Hydro road) - the prices for these olives/hoses/sets are ridicilous. So I had good look at both. shimano (brass-) olive and (stainless-) pin should work absolutely fine on sram/avid hoses. The cone of the housing/screw that actually presses the Olive onto the hose are the same (Diameter of the hose also). This only accounts for the standard (silver aluminium - black pin) avid/sram hose olive. These Red ones "stelamajjig" or whatever (i only know of etap road) - i have these here - are a bit different but i don t have the corresponding etap levers. Somwhere someone wrote that these may press a valve when mounted - with the standard ones these valves would stay closed. regards from berlin