Learn Dutch: Een hond is heel trouw.

In Dutch, any 'd' at the very end of a word is pronounced as a 't'. So hond sounds like "hont". If you make the word plural (honden), the 'd' moves to the middle of the word and goes back to sounding like a regular 'd'.

Can I use erg instead of heel to mean "very" in this sentence?

Yes, you could absolutely say Een hond is erg trouw. Both heel (which literally means "whole") and erg are used to mean "very". They are completely interchangeable here, though heel is slightly more common in casual everyday speech.

Is the word trouw related to the Dutch verb for "to marry"?

Yes, it is! The verb for "to marry" is trouwen. The adjective trouw used in this sentence means "loyal" or "faithful". You can easily see how the concept of marriage and being faithful share the exact same root word in Dutch.

Does Een here mean "a" or the number "one"?

Here it means "a" (or "an"). As the article "a", een is pronounced with a short, unstressed "uh" sound. If you specifically meant the number "one" (as in exactly one dog), it would be written with accent marks as één, and pronounced with a long "ay" sound.