Are you an experienced hire or a junior one? Experienced hire go throw your resume to people on linkedin / efinancialcareers and let those headhunter try and match you to jobs. If junior ... honestly quite difficult because there is no lack of junior level hires locally.
Tender after EP approved lor. Generally it takes few days to couple of weeks. Mine last time took 2 weeks whereas my wife one took I think 2 or 3 days only.
If you want to do it the "clean" way then ask your current malaysia company to issue borang CP21 for you. Then u bring it to LHDN and close off your income tax file. If can't-be-bothered way then every year just declare zero income on tax filing lo. Welcome to SG and if you're interested send a PM to our daikor MacKiddo to get added to the m'sians working in sg support group whatsapp