Apple - Can anyone recommend an app for creating flowcharts and diagrams?

For free online diagramming there's diagrams.net, which I am a developer on. It supports the automatic connection and dragging of components you're looking for. Also, it's free (and open source), which meets your under $30 requirement.

There is also a Desktop version available.

If you can stretch your budget, get OmniGraffle for Mac. At $100, it's pricier than you'd like (do you possibly qualify for the $60 edu price?), but it's exactly what you're looking for.

On the lower end there's Mindcad Incubator for $50, but I haven't tried it myself and I'm not sure it does everything you want.

The Google Docs suite of tools now has a diagramming tool that lets you create flowcharts. While not as feature rich as something like OmniGraffle, it does cover all your requirements: simple & clean interface, basic shapes (and not an overabundance of shapes), automatic connectors with elasticity, and it meets your price point at free.

Certainly can't hurt to try it out before you drop $100 on the Mac Daddy of diagramming programs for Mac.

Edit: just noticed your last paragraph in your question. Not much I can do about the UI, but I will mention that offline support is about to make a return via Chrome.