1: question can we do conjugal process since the barrier is that im married here in the Philippines
2: and my document here in the philliphine is single name
3: 2017 we try trv I refused could be affect in our conjugal application
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And for the living together its impossible becouse my partner cant go here in the Philippines becouse of work
A key point: did you _ever_ live together, continuously, for more than 12 months? If so, it may be possible to file under common law, even if not currently living together. Note, you would need to have quite strong documentation showing both that you were living together for that period and have remained in that relationship since. (The fact that you've lived apart for four (?) years doesn't help, but it may not disqualify you).
1. I believe you are right that in some cases, conjugal sponsorship from the Philippines is possible (due to the near-impossibility to divorce and remarry). I don't know the details well, but there have been discussions here before and you should check carefully before submitting. You may want to consult a lawyer because the specifics of what is needed to demonstrate the "barriers" to marriage/common law are so specific. Eg there is a process for annulment, I believe, and you may need to prove/document why annulment is not possible (I'm not clear on the details). You'll also need to demonstrate why you can't live together and become common law (e.g. TRV refusal is one such step).
2. Single name is not an issue apart from being careful about documents (Canadian docs and forms will generally want the single name used as last name, not first name).
3. The refusal of TRV will not affect the conjugal app (or most family sponsorship cases), unless of course the refusal was for some worse reason (criminality or security concerns). Oddly the refusal may be required in your case, because you'll need to show why you can't become common law (e.g. you can't physically live together because you can't get visa to Canada).
Unfortunately I don't know that much more about the specific case of marriage/Phillipines. There are other threads here on this (you may want to try searching for annulment as that seems to come up frequently in the Phillipines cases for conjugal).
Either way (common law if. you did live together or conjugal) it may be a difficult case to document and you should consider working with a lawyer (whether throughout or at least getting some consultations).