Boutique Firm in Singapore or BO in Toronto?

Hello, I’m pretty new here and I need a career advice. I am 26M Canadian. I am stuck in a situation where I have to choose my decision.

Bit of my profile here, I graduated from one of three big schools in Canada (UBC/UofT/McGill) and currently working for a foreign bank BO in Toronto.

I received a job offer from a boutique P/E firm in Singapore and starting in September. Salary is around 6500 SGD for base plus incentive bonus.

Second, I am having interviews with three consulting firms, one from tier 1 firm and two from tier 2 for Tokyo office.

Third, I am going through a process to work for public sector in Canada. (Kinda like last resort)

My goal is to jump into Investment Banking by doing MBA for Top 15 US school.

I am having an issue here because P/E firm is rushing me to join and I have to answer to join or not by mid August.

I have few questions here. 1) is it actually true that I cannot move back to private sector from public sector?

2) can I just accept the offer from P/E firm and move into consulting after few months working at P/E firm? I never thought P/E firm wants me to join this quickly. I thought the process would take much longer.

3) I already job hopped once when I quit my first job after a year. If I switch my job now, this will be my second job hopping where I will quit my job in two years. Is this disadvantageous to find a next job?

4) if I work one more year at current BO, will I have better opportunities to find another job at FO?

I apologize for your trouble. I want to hear what others will take facing with multi decisions like this.

Thank you for your help.