Partial answer (various details missing, big picture and most details are there) [EDITED later to add:] Still incomplete but less so, thanks to several nice observations from hb20007 which I hope they don't mind my transferring (with credit) into this answer. It turns out that I made an incorrectly narrowing assumption before.
Friends or foes?
Friends, but alas false friends despite the Romance.
This puzzle is about
words in English and various Romance languages [EDITED to add: it turns out, not only Romance languages, but they are all European languages so far] that look like one another but have different meanings, which are sometimes called "false friends" or equivalent phrases in other languages. In a couple of cases, the two divergent meanings are actually in the same language.
If we
read off the initial letters of the answers, following the lines and ignoring the distinction between U and V (since some of the words are Latin), we get FALSE FRIEND in black, FAUX AMI in blue, FALSUS AMICUS in red, FALSO AMICO in green, and FALSO AMIGO in yellow. English, French, Latin, Italian, Spanish. I haven't found perfect matches for everything in those languages and for that matter I don't think I've needed to use French at all. [EDITED to add:] It turns out that some other less-related languages are also involved here.
Center of the hearth?
FOCUS = centre in English, hearth in Latin.
Year ring? Yes!
This must be AÑO = year in Spanish; similar words in other Romance languages mean "anus" which I guess is sort of a ring; there is also e.g. "annulus" which means a ring in Latin and also (mathematical) English; but I think I am missing at least one thing here. (I also don't see anything meaning "yes"...)
Crazy place?
LOCO = crazy in colloquial English; = place in Italian.
Sound sleep?
SONO is sound in Italian. Various similar things mean sleep; e.g. SONNO also in Italian. Again I think I may be missing some specific word. [EDITED to add:] hb20007 observes that SONO is sleep in Portuguese.
Summer house?
ESTATE = summer in Italian, = house (kinda) in English.
Twenty winds?
VENTI = twenty in Italian, = winds in Latin.
Wave hello?
OLA = both wave and hello in Spanish. [EDITED to add:] hb20007 corrects me: there's an H on the start in Spanish, but OLA is hello in Portuguese.
Ten times an unknown?
X = ten in Latin, one symbol for "times" looks a bit like an X, and X is a common choice of name for an unknown quantity in mathematics.
Only ground?
This must be SOLO or SOLA, both of which are possible forms of words meaning both "only" and "ground" in Latin. They also mean "only" in some other languages.
Strong by chance?
FORTE = strong in Italian, = by chance in Latin.
Soul-nourishing apple?
This one puzzles me. We need a word beginning A. The words for apple in the non-English languages here fall into two families, typified by "pomme" in French and "malus" in Latin; I don't see any A-words. And we have anima/âme for soul, maybe, but "nourishing"? Not sure what's going on with this one. [EDITED to add:] hb20007 observes that ALMA is soul in various Romance languages and means apple in Hungarian.
Broken wheel?
ROTA = broken in Spanish, = wheel in Latin.
Known evil?
Another one I'm puzzled by. It needs to begin with M. MALUS is evil (as well as apple) in Latin and there are close relations in other languages, but I've not found anything that means "known". [EDITED to add:] hb20007 observes that MALUM means "known" in Turkish.
Go mad?
I think this must be IRE = go in Latin and = anger in English. "Mad" means "angry" in US English; it doesn't really mean anger. But maybe it's close enough.
This eastern evening?
I think this must be ESTO or ESTA, which mean "this" in Spanish and seem as if they might well mean "eastern" and "evening" in other languages -- though I haven't actually found any where they actually seem to... [EDITED to add:] hb20007 found the details: ESTE is another version of "this" in Spanish, where it also means "east", and it means "evening" in Hungarian.
Expensive meat wagon?
CARO = expensive in Italian, = meat in Latin, and surely there must be some language in which it's related to the English "car" (or maybe the point is just that it sounds like it might be).
Celtic cock?
GALLO = Gaulish in Latin, = cock (in the sense of "rooster") in Italian.
Bare knot?
NUDO = naked in Italian, = knot in Spanish.
B-side?
Another one I don't get. It needs to begin with U or V. VERSO in English = the back side of a page, but that's a single definition; in various Latin-derived languages the word means things related to turning but (I think) never quite "side" and certainly not "B".
Hour mouths?
ORA = hour in Italian, = mouths in Latin.
Round house?
DOMO = dome in Italian, = house in Latin.
Witch story?
Another one that puzzles me. It needs to begin with S. Witch is STRIGA in Latin, STREGA in Italian -- right first letter but too long and no "story" meaning so far as I know. The only Romance-language "story" word I know of beginning with S is STORIA in Italian: too long and nothing to do with witches. SORCIERE in French begins with S but too long and nothing to do with stories. Unless I missed one, none of the translations for "witch" offered by Google Translate in any of the languages it knows will fit here.