So can I assume that "I" in Welsh is "dw i"? Or is it just "i"?
The word I in Welsh is i, fi, mi depending on context - it's i here.
dw is a form of bod (to be) - it's a bit as if Welsh sayd "I am wanting soup" or more literally "am I wanting soup".
'I am'= Dw i
and 'I' is the i in this case.
There is also another i in Welsh, a preposition meaning 'to, in order to, for', etc.
eisiau is a noun meaning 'a want, a need':
It is just "i" but if you have this in a sentence like for instance this. . . "Dw i eisiau" you dont just put it like that its very lazy to the people if you think about it, so people put like this instead "Dw'in eisiau".
Dw i eisiau ... is correct - 'n/yn is not used with eisiau.