Macca
If you're coming here to work then you will need an Employment Pass. If you don't have one then you can't rent an apartment, get a phone line, get utility connected. Ok, your co could do this for you, but they have to declare who they are paying it for.
If you do the tourist visa thing then you always run the risk of not getting back in, or having lots of questions on why your trips here are so frequent. I know someone who got stopped as he went back and forward to Malaysia, had to pay lots to be allowed through and then had problems each time he tried to move around. Big Brother is watching. Just get the visa - your company applies for you and it is easier if you have a regional role to play.
On your earnings, the official tax position is that tax is payable on earnings paid in Singapore. In theory you can get around this by having them paid offshore, but any ATM withdrawals or cash brought into Sgp are taxable. It's also evasion, not looked on lightly and your co would get into trouble for facilitating it. Tax is low here. Just do it properly and pay it.
You're liable for tax if you have worked in Sgp for more than X number of days (I think it's about 83 - check the iras website www.iras.gov.sg). So even the tourist visa may not help you here. And if you only work for a short period, then the tax rate is a flat 15% rather than the stepped rates which would average at 10% for a $100k salary.
Yeah, it's nice to try to beat the system and get away with not paying tax or applying for EP in the proper manner. Is the stress really worth it? Face your responsibilities and do the whole thing properly. Like the rest of us.