Your wheel is safe in the dropouts but it allows no room for slippage. If you can add a link (or half link) and get the axle further into the dropouts, you'd at least feel a lot safer (I'd do it).

I'm not sure what's happening with that chain, but the pin shouldn't look like that so something isn't right - you should really struggle to pick which link you've just joined.

Bike mechanics are humans just like the rest of us and while some are idiots, most are happy to help, to advise or just chat about bikes. Building a relationship with your lbs will pay more in pleasure and advice than you'll ever save over the internet.