“Familiarity breeds contempt.”- is it true?

Yes, it is true..when two people come to know more about each other..there are things which you like and dislike about the person..so being familiar leads to some amount of contempt.

It varies from person to person. But if the person is not having any ego nothing happens

Excessive closeness is harmful to relation. Anything in extreme harms. There should be reasonable closeness with neighbor and others. If you cling too much to anyone, relation may be spoiled.

It is not always the case. Yet it is also true that as you get more close to a person, you get to know a lot of many things about that person, some of which you may like and some of the things you might not like and even come to despise them. The key to a relationship of any kind, is to accept the person as he or she is and not try to change that person to someone he or she is not! Since the expectations run both ways, it is also equally true that the reverse may be the case for that other person too, who may not like certain things about you.
So to avoid your relationships going the way of contempt through excessive familiarity, accept the person the way he or she is and not to keep any undue or unrealistic expectations from that person.

That is very true. For some days, when I could not meet my friend, I missed him a lot. But when we started meeting after some days, he started visiting my house daily and honestly, was a disturbance in my work. Yes, familiarity does breed contempt.

Not necessarily, it can breed otherwise also.

Not always, but sometimes it can happen. In many cases people tend to take those who are close to them for granted because they are always there...

This depends on person to person. I feel that their must not be jealousy or ego in any relationship.

there should be no ego in relations

not neccesaary

This depends upon individually but there should not be any ego.