Not surprised by the nasal violation, they wouldn’t want to be blamed for not doing a good job, and if that means you lose a few neurons, so be it.
Probably the closest wet market to you would be Tiong Bahru, and it is a popular one:
https://goo.gl/maps/CtLZQVUVhvCrMsJb9
From what I understand, there isn’t much room to haggle - there isn’t as much of that in Singapore unless it’s a big ticket item or you’re buying in quantity. If you are Caucasian, there is always a risk of a skin tax (higher price than locals), but even my wife pays higher prices because she likes to dress above average - she just treats the extra price like a charitable donation. But what you should do is ask the price upfront and closely observe locals, see what they pay and expect the same. That said, it’s not likely they will try and rip you off too badly, after all, you can just hand it back and say no. Note that prices in wet markets are not necessarily cheaper than in the grocery store, because the higher quality and freshness can have a premium associated.
I do know some locals who never cook - it is possible here because cooked food outside can be cheaper than eating in (just the opposite compared to the US). When I first moved here I ate out the majority of the time, but after having a family and a live-in maid, we now eat in more than we eat out. In fact I’m sitting down right now to eat a grilled Cajun chicken breast with mashed potatoes and beets that my helper whipped up for me.