1. I will be in Australia till July. In that case I may apply from here. I have to contact high commission of Canada in Australia and explain my situation right? I am in tourist visa btw
It will be advisable to apply at the home consulate, which for Bangladeshis is the CHC in Singapore.
2. In case I do apply online, what about my passport? Won't they require it?
Yes they will ask for it at a later stage of the application.
3. I would like to ask a question of mine again that went unanswered. I got into both calgary and ubc. Fund requirement for calgary is less and I can show it. Is it wise to get the calgary study permit and then request a transfer? How will it be shown and how do I request the transfer?
Since you are not funded, there is a chance that UofC might inform CIC about it. And if CIC figures out you are going to a university which costs more than you showed then it might be a problem for you.