If you file a SAR for a retired Housekeeper, do you mark private household as the NAICS code?

No. That NAICS code is used for the "business" of running a household. Think of a butler, maids, the Downton Abbey concept. If you're filing on the erstwhile housekeeper, you don't use a code. Put "retired housekeeper" in the field for the occupation or business.

For hairstylist, I put health and service. Does this sound ok? If not, what would be better?

The NAICS code for beauty salon (ie hair stylist) is:

812112 Beauty Salons

This U.S. industry comprises establishments (except those known as barber shops or mens hair stylist shops) primarily engaged in one or more of the following: (1) cutting, trimming, shampooing, coloring, waving, or styling hair; (2) providing facials; and (3) applying makeup (except permanent makeup).

Cross-References. Establishments primarily engaged in-- •Cutting, trimming, and styling mens and boys' hair (known as barber shops or men's hair stylist shops)--are classified in U.S. Industry 812111, Barber Shops;
•Offering training in hair styling or the cosmetic arts--are classified in U.S. Industry 611511, Cosmetology and Barber Schools;
•Providing nail care services--are classified in U.S. Industry 812113, Nail Salons;
•Providing massage, electrolysis (i.e., hair removal), permanent makeup, or tanning services--are classified in U.S. Industry 812199, Other Personal Care Services; and
•Providing medical skin care services (e.g., cosmetic surgery, dermatology)--are classified in, Sector 62--Health Care and Social Assistance.

http://www.census.gov/cgi-bin/sssd/naics/naicsrch?code=812112&search=2007 NAICS Search

Since you can only use one from the list, back up the number until you find one on the list (ie truncate the last 2 to 3 numbers from the actual NAICS code). In this case, you would use the subgroup 812 Personal and Laundry Services.