Mögen vs. gern
I seem to recall that the adverb "gern" is used to express fondness for an activity (or verb) rather than "mögen." So, for instance, "I like to swim" would be translated as "ich schwimme gern"; however, I noticed that the only translation of that sentence that is accepted here is "Ich mag schwimmen." Is it acceptable to use either "mögen" OR "gern" to express fondness for an activity? Is one more idiomatic than the other?
You're absolutely right about "gern". "Ich mag schwimmen" is not idiomatic in German. You can't use "mögen" with another verb. "mögen" can only be followed by a noun or a pronoun.
So could one say: "Ich spiele gern Golf." and "Ich mag Golf zu spielen."
Are these both grammatically correct and do they express the exact same thing?
This is a bit subtle, but I think in this sense, it should be either "ich mag Schwimmen" with a capital S (das Schwimmen), or "ich mag es, zu schwimmen" (extended infinitive). But yeah, "ich schwimme gern" definitely sounds more idiomatic.
Note that you can also use "ich mag schwimmen" (with a lowercase s) colloquially. That'd mean something like "I feel like swimming." This usage differs regionally though, I believe...
Hope this helps :)
Or in things like "Es mag regnen. - It may/might rain" or "Das mag sein - That may be."
Sorry to bump the thread (not sorry), but I wanted to (re-)raise awareness of this point. It says in the description page of "Verbs: Present 1" currently that mögen cannot be used with another verb; and I wanted to point out the correspondence with "may/might", but it seemed right to see whether anyone else had ever brought it up before. Indeed, I found this post.
I appreciate that this "may" aspect is out of scope of that particular lesson, but I can't help but be frustrated with the half-truth that's in that distraction, and wonder whether it might cause more harm than good if German-learners then experience the usage in real life, not only having no idea what it means, but indeed being essentially convinced that it's not valid in the first place!