Children's Theatre of Arlington has announced auditions for two productions. Tryouts for the musical "Hansel and Gretel" will be held for children ages 9 to 14 from 4:30 to 6:30 p.m. Monday and Tuesday. Auditioners should prepare and bring a song to the tryout, or they may sing one that will be provided. For more information, call evenings at 824-1715. Youths ages 12 to 18 are encouraged to try out for "The Tamarin Trickster," a Brazilian play, from 4:30 to 6:30 p.m. on Jan. 20. No preparation is necessary, but call for an audition appointment at 525-2992. Auditions for both productions will be at Gunston Arts Center, 2700 S. Lang St., Arlington.

Apply for a summer job as a park ranger at Fredericksburg and Spotsylvania National Military Park by Jan. 15 and learn how to tell park visitors about the history of the battlefields, help with resource management projects or become a leader in the Youth Conservation Corps. Applicants must be at least 18 or a high school graduate and must meet physical fitness and work experience requirements. For more information and an application, call (703) 373-4461. Mail completed forms to Seasonal Employment Unit, National Park Service, P.O. Box 37127, Washington, D.C. 20013-7127.

Come to a quilting bee once a week this winter and complete a quilt while exchanging tips and conversation with other quilters at Providence Recreation Center, 7525 Marc Dr., Falls Church. An instructor will be on hand from 10 a.m. to noon every Wednesday from Jan. 20 to March 9. Register by Sunday for all eight sessions by bringing $40 to the center, or register by phone one week before each class for $5.50. For more details, call 698-1351.

The Jewish Genealogy Society encourages anyone interested in tracing family heritage to attend its next monthly meeting on Sunday. Featured will be "Other Ellis Islands," a discussion of immigrant arrivals in ports across North America, led by a staff member of the National Archives. The talk is free, and begins at 2:30 p.m. at Beth El Hebrew Congregation, 3830 Seminary Rd., Alexandria. Call 938-2840.

"Questions Homebuyers Ask and Seminars to Answer" is the title of a series of free weekly seminars for Virginia residents that begins Wednesday, sponsored by Consumer Housing Libraries. "How to Make Real Estate Your Career" is Wednesday's topic, and will be followed this month and next by seminars on understanding real estate contracts before signing, getting through the settlement process, purchasing real estate as an investment and choosing a real estate agent. Consumer Housing Libraries is not affiliated with any agent, builder or developer. All seminars start at 7 p.m. at 11166 Main St., Fairfax. For information, call 273-9866.

Find out what's on the Virginia General Assembly agenda for 1988 at a hearing Monday at the Arlington County Court House. The hearing will be held by the Arlington County state legislative delegation at 7:30 p.m. in the county board room, 1400 North Court House Rd., Arlington. For more information, call Elizabeth Gawron at 558-2401.