Can I trade US Counters through POEMS if I am a US Resident/ US Citizen /Canadian Citizen?

No. US Citizens or US Residents are not allowed to trade in US Stocks through PSPL.

Can I continue to trade in US markets if I subsequently become a US Resident/US Citizen/US Taxpayer?

No. Once you are a US Resident/US Citizen/US Taxpayer, you will not be able to trade in US Stocks through PSPL and you are required to notify PSPL should there be any change of your citizen/residency status.