"Fonn" is a melody, "fonn mall" = slow air. Terms for dance tunes are also generally translations and/or transliterations of the terms we use in English. "Port" is a bit confusing, as it can mean a jig or any lively tune. There are various subclasses of jigs, "port singilte", "port dúbailte", "port luascach" are single jig, double jig and slip jig respectively

also port béil = lilt; port a' bhéil (port-a-beul in Scotland) = mouth music (songs to dance tunes)
Luasc-cheol = swing music; snagcheol = syncopated music, jazz
Ríl= reel (although in dancing a reel is "cor"); cornphíopa = hornpipe
máirseáil = march

I've been using "sleamhnán" for a slide, but I'm not sure that's correct. People understand me, anyway.

"Garbhchríoch" means highland, but I don't know if it's used to refer to the tunes; I have heard people say "highlands" in English when talking in Irish about music. A highland is similar to a "sraith-spé" (Strathspey, though a lot of people now refer to that region of Scotland as "Speyside"). And you wouldn't translate "mazurka", though you could spell it "masúrca".

I found some dance terms in "Foclóir Ceoil", a slim dictionary of music published by An Gúm, including
fáine (ring) = circle
rince mór = round dance
rince fada = long dance [progressive dance?]
portchéim = jig step
sleaschéim = sidestep
slabhra = chain
ar aghaidh is ar gcú = advance and retire

I don't see "ciseán", a basket, which is the word we use for a swing (luascadh) with 3 or more people; called a "Christmas" when calling in English for set-dances.

In the north we tend to say "damhsa" (sounds something like "dowsa") rather than "rince" for dance.

There are also some older Gaelic classifications of music & song
suantraí = lullaby, soothing slumber music
geantraí = cheerful, laughter music
goltraí = lament, crying music

caoin, caoineadh = a keen (wail, lamenting song), keening

The Irish spelling of planxty is "plancstaí"
"plearaca" = the humours of ...

piping = "píobaireacht"
singing, chanting & even complaining! = "cantaireacht"
plainchant = "cantaireacht eaglasta" or "cantaireacht reidh"