Translation:It is hard to sing this song.
I'm not certain, but my intuition is that doing something that is たいへん requires great effort, while doing something that is むずかしい requires great skill.
That's about right.
むずかしい can also be translated to "difficult" or "complicated".
While learning a new language can be "たいへん" sometimes, a grammar point is not. But some of them are "むずかしい" nonetheless. ^^'
I thought basically that adding の after the verb was equivalent to adding "ing" to it. That is, changing "sing" to "singing"? But I put "It is hard singing this song" and was counted wrong - in favor of "It is hard to sing this song." Should both be correct? Or is my fundamental understanding out the window?
That the problem in to not study grammar. The の after a verb turn the verb into a noun, so 食べる means "to eat" while 食べるの means something like "the act of eating" or just "eating". In some sentences it would be irrelevant but basically that's it.