Can a single pole (normal/regular) circuit breaker be used in spots designated for tandem?
Can a single pole (normal/regular) circuit can in spots designated for tandem? 

I have to retract my earlier answer to this question.  I had bad information.  Yes, standard breakers can go in tandem permitted slots.

Almost like backward compatible; the circuit breaker can accept normal/regular or tandem. You typically use normal/regular until you need to upgrade to tandem?

You use tandem to save space and run extra circuits when you have no more room in the box.  It's faster and easier than setting up a sub-panel or putting in a larger box, but it might lead to you using more power than your box itself or main feed is rated for.

What does it mean that the circuit breaker was oversized?

That the breaker allowed more amperage than the wire could support.  If you run a 20A breaker over 15A wire you can end up causing a fire.

I probably frustrated you calling it a normal/regular circuit, what is it actually called?

A circuit breaker.  The language you used is fine.

Are there are other general rules I should know?

This is really too broad to answer...  we don't know what you DON'T know.