Many sinks have a slight lip like that, but impossible to tell from the photos if it could be uninstalled, cleaned up, and reinstalled a tad lower using less sealant. You're simply seeing dirt settling there out of the little bit of water that sits there after use.

The problem is not due to that side drain pipe unless it is pushing through so much water that the sink backs up. But what is that side pipe there for in the first place? Is it some hillbilly hookup for a washing machine? It looks like a bogus hack by someone who isn't concerned about code compliance.

The handyman who installed the drain used Silicone instead of plumbers putty.

Is that a plastic drain? My limited experience is that plastic drain assemblies have a higher lip than metal drains, probably because the weaker plastic needs the extra thickness for the same/similar strength.