More often than not these would be drivers grabbing a quick bite to eat while their employer(s) are having dinner (elsewhere), conducting business or entertaining.

What kind of things are you shopping for? Someone mentioned the Platinum Mall, on Petchaburi Road (nearly adjacent to Panthip Plaza, across the street from the Amari Watergate hotel), for clothing, and it is nice because it is air-conditioned, and huge ( 6 ~ 7 floors with a hundred shops on each floor). However, for even better bargains on clothing, and a unique experience, cross the street and shop at the Pratunam Market. Thousands of tiny shops, essentially surrounding the Amari, enclosed overhead but no aircon, where it is easy to get lost. There are also a few multi-story clothing malls opposite Platinum (called "City Complex").

For restaurants the choices are endless but you should probably try one that serves "Royal Thai" (or Royal Court) cuisine. Bussaracum comes highly recommended by some FTers.

Regarding ice and water I'd say that ice everywhere is generally safe as it is made at central plants with filtered water and delivered everywhere (nearly every street stall will have or share an insulated box with delivered ice). Like all Thais, I stick to bottled ("Naam Pow") or filtered water, the city water supply is variable. Sometimes it smells very, very bad (sulfur/rotten eggs) where I live, most times it's OK. I use it to shower, wash dishes & clothes, brush teeth and that's about it.

Street stalls would use filtered water, from machines, for cooking but tap water for cleaning. They use 3 or 4 step cleaning process (in tubs on the sidewalk), one of which involves some sort of bluish colored additive, presumably for sterialization. Eating utensils can be challenging, sometimes there is a pot of boiling water nearby (in coupon food courts) where you can dip the spoon, fork, chopsticks, etc. to sterilize. At a street stall you just wing it or carry your own?