"Caballus" is actually a loan into Latin - most likely from an ancient Celtic language.https://en.wiktionary.org/wiki/caballus
There are some Celtic loans into Latin that were subsequently reintroduced in Irish and Welsh (and English!) rather than coming directly from proto-Celtic, such as "cloccus" (bell) > cloch, clóg, "clock", or "currus" (chariot, wagon) > car, carr, "car".
But ceffyl and capall look more or less the way you'd expect if they'd been retained from Proto-Celtic, rather than being loans from Latin. And the Romans took a lot of terminology relating to horses and transport from the Celtic languages.
I have a horrible habit of translating 'eisiau' as 'need.' Just for information, am I far wrong?
The GPC seems to think so - http://geiriadur.ac.uk/gpc/gpc.html?eisiau. It's translated as "want", "lack", "deficiency" and so on (bear in mind that it's a noun, rather than a verb). The course creators may have a preference for "want" though, to keep it separate from anghen (need).
On a side note, anghen is like eisiau in that it's a noun - so you don't put yn in front of it.