To a native American English speaker, all of these sentences sound a little strange, even if they may be grammatically correct (I'm not 100% sure). If I were to rephrase the sentences so they sound less awkward, I would say:
(a) We can encourage each other using music.
(b) I can't quite rephrase this one to sound right.
(c) We can encourage each other through words.
(d) We can encourage each other with love.
(e) We can encourage each other with winks.
(f) We can encourage each other via gift exchange.

As in the correction I gave for (f), all of these will sound more natural if you complete the sentence with a verb phrase rather than with a noun phrase. The preposition before a noun phrase is more likely to be "with" than "by."

Thank you very much! "By" is sounding more and more interesting to me. It might make for the next topic I do research on.

I think you would have to use the preposition "with" for all of these.

If you changed it to:

We were encouraged by the music, by the words, by the gifts.....

but the article is not optional in those implying that we are reporting on the effect of particular things not just things in general.

The other option is to use the -ing form after by:

We can encourage each other by winking
We can encourage each other by exchanging gifts

But that doesn't work for all the examples you give.