Having the thoughts of working part time in Singapore is actually good, but the chances of getting hired just to work part time can be equal to 0, because the employer need to pay and apply the work permit for u.

Also, if u work less than 183 days, you are taxable as a non-resident at 15% flat.

Relax bro, it is normal that you don't receive much replies at this month because it is already year end and people tend to wait for bonus before resign. Trust me that next early year will have more jobs opening. In the mean time, try improve your resume so that it look nicer.

And for the result yet to released, it is ok but once you obtained your result, you need to submit to your HR. 

Right now.....for these few more months...I would say around 80% if not higher all the work permits/employment passes has been rejected. DONT EVEN THINK of applying PR. Even getting a work permit/EP would be considered lucky.

Dont forget when u do get a PR u will have to start contributing to CPF