No. sy'n would be used with an adjective, a noun or a verb-noun:
- Sioned sy'n dal - It's Sioned who is tall
- Sioned sy'n ffermydd - It's Sioned who is a farmer
- Sioned sy'n gwerthu'r gwartheg - It is Sioned who is selling the cattle. (Note that gwerthu is a verb-noun, not a verb)
piau/biau is a very irregular verb ('it is who owns'' = 'owns'), not a verb-noun, so no yn and, strictly, no sy. In the colloquial language, however, sy often gets put in there as well, even though it has no true grammatical function in this construction:
- Sioned (sy) biau'r gwartheg - Sioned owns the cattle.
Traditionally, perhaps, but in modern English 'It is me' is the usual dayt-day form and the form that is nowadays taught to learners of English. That matches the day-to-day register of Welsh taught on this course and on the introductory and intermediate courses in the DysguCymraeg scheme for adult learners of Welsh in Wales.