Are these technically last names? Oftentimes Indian passports with these names are all on one line -- just first and "middle" name, nothing under "Surname". So what are "Singh" and "Kaur"? The only thing I know about them is that "Singh" is for men and "Kaur" is for women.

Also, what's the deal with "kumar", "ben", "bhai", etc.? They are added to names for... what? What are the differences between these suffixes?

"Singh" is a name given to all Sikh men (and considerable numbers of Hindu Jats and Rajputs), and "Kaur" (restrictively--it's generally not found outside of Sikhism) to all Sikh women.

"Kumar" means "prince", common epithet.

"Bhai" means "brother" (mostly used for addressing, not the name itself)

"ben" means "sister" (detail as with "bhai")

As far as "surnames" go, it can be somewhat difficult to explain. Many South Asians (ubiquitously) use their "native village" name as surname (so you get "Mantek Singh Attariwala", meaning "Mantek Singh, native of Attari"), but some do not.