It’s actually /tsʲ/.
How do you tell if its doua or doi?
două - is used for feminine cases: "Două femei. Two women
doi - is used for masculine cases: Doi bărbați. Two men.
Are these distinguishable in spoken Romania? The plural almost had a clicking sound at the end.
Yes, you can definitely hear the difference in spoken Romanian.
one man, two men
so you dont pronounce the 'I' at the end of barbat?
Yes, you do but it's a very, very short "i"