Is it true vagina closes if woman is not sexually active or not having sex since long time?

Myth. Unless there atrophic change of menopause, the caliber of the vagina stays the same. Lack of intercourse and change in new partner's anatomy may give the impression of tightness. This improves as the couple gets use to the coital activity.

Related Questions

I'm a 19, female. I've recently become sexually active, after the last time having sex, I've noticed dryness in my vagina, and discomfort.

Extended foreplay. I would suggest the following: first and foremost protect yourself with BC pills and condoms. Sexual lubrication can be enhanced by prolonged 15-20 minutes of foreplay and intimate touching of all erotic areas. You must communicate what feels good (or fantastic) to your partner. Please take your time and remember that "outercourse is more important than intercourse" I would give this a month.

Is it normal for slimmy stuff to come out of the vagina during a period? I'm not sexually active.

Probably. During the menstrual period you will pass blood, clot, tissue fragments, and mucous. Sometimes the entire endometrial lining will pass at one time - that is called an endometrial cast, and is not abnormal. What you describe is likely perfectly normal.
Yes. It is normal to have a variety of vaginal secretions during the month. Near the time of ovulation, those secretions become very slimy and stretchy.

Is a normal for vagina to be itching everytime my period is finish. I'm not sexually active?

Yes. There are some changes in the levels of yeast in and around the vagina with the hormone changes of your period. Try applying mineral oil to the outside when you have your period.
Yes. Some women will experience cyclic bacterial or yeast overgrowth, frequently this will occur at the time of the menstrual period. Often the symptoms resolve without treatment. Some female sanitary products (pads/tampons/etc) contain perfumes and/or deodorants which can cause an allergic reaction, which could also explain the type symptoms you are describing.