is "eisiau" pronounced with an "h" of English? I hear it sometimes as "eysie-eye" and other times as "eyshe-eye"...
I pronounce it with the "sh" sound in the middle because an "si" is how that sound is represented in Welsh. (A good example is how "Shop" is "Siop" with the same pronunciation.
The trouble with the "eye-s(h)ee-eye" used in the recordings is that it's a phoney spelling-pronunciation that you're never likely to hear in real life.
As Gareth King says, in his Modern Welsh Dictionary:
"This word is variously pronounced isie, isio, ise [=] - but never as spelt!"
[=] approximately: ee-sheh, ee-shoh, or ee-seh
We is "Ni" pronounced like "knee" in English. "Hi" means "She" and is pronounced like "He" (make sure you don't get confused since it's pronounced the same as English but means the opposite). "He" is a little more conplicated. The northern word is "Fo" and the southern word is "Fe" though in some instances these become just "o" and "e". There's also a third form "ef" though this isn't used much and you don't have to worry about that for now.
Without it there would be no verb in this sentence, and you are right that "Dyn" means "Man" with a long vowel, but with a short vowel it means "Are". The Welsh comes from the phrase "Dyn ni ag eisiau pasta." which literally means "We are with a want of pasta" though the "ag" is not used today.