Oil light issues and not starting

Good morning.

I was wondering if I could ask questions about two issues my car is a SHO.

the oil light comes on and chimes when I have driven for a while, and then either come to a complete stop or slow down to about five mph (as on the freeway). When I get home the engine smells like oil is burning. However, after my mechanic plugged in his computer to diagnose, nothing comes up, no codes, nothing. I have read posts/blogs that it could be something as simple as an IAB sensor, to something as serious a the rods are going out (ugh).

The other issue is that there are times when the car wont start. Battery is fine, the dash lights up, just won't start. Has the push-button ignition on the dash. I have changed the battery in the remote, still has not resolved the issue. There are times when we have had to sit in my car for over twenty five minutes, just waiting, and then finally it will start and I can resume my driving. However again, nothing shows up on a diagnostic. And at $125.00 per visit to the dealer for the diagnostics, this is getting frustrating.

Any ideas or help you can offer?

Thanks much!