Question about how to understand this sentence.

Immaculate red and white tables dot the second-floor walk-up business that's usually full of Peruvian immigrants at lunchtime. (original)

My way to understand the original is :
On the second floor ,there is a "walk-up business".
(the "walk-up business " here is perhaps a window where there are many people , the window is used to serve such people to deal with their business)
There are many immaculate red and white grids around the "walk-up business" .
Usually ,there are too many Peruvian immigrants at the "walk-up business" at lunchtime.
They are queuing up for dealing with their business.
Question: Is my guess correct according to the original?

Question

Question about how to understand this  sentence.

Immaculate red and white tables dot the second-floor walk-up business that's usually full of Peruvian immigrants at lunchtime. (original)

My way to understand the original is :
On the second floor ,there is a "walk-up business".
(the "walk-up business " here is perhaps a window  where there are many people , the window is used to serve such people to deal with their  business) 
There are many immaculate red and white grids around the "walk-up business" .
Usually ,there are too many Peruvian immigrants at the "walk-up business" at lunchtime. 
They are queuing up for dealing with their business.
Question: Is my guess correct according to the original?

Answer

“Walk-up” refers to walking up a flight of stairs. New York apartment buildings with no elevators are called “walk-ups”

“Full of” just implies the establishment is full, there’s no connotation of “too many”.

Hope this helps!

Answer

Walk-up business to me suggests that you don’t need to book, it is just a simple eating place.

The red and white tables (maybe they have clean red and white tablecloths) are scattered around, maybe in no particular arrangement.

The Peruvian immigrants eat there because it is cheap. It isn’t too full of, it is just popular with them. Maybe it is run by a Peruvian and sells food they like.