What is the relationship between Romeo, and his parent?
It is obvious that his parents loved him, but they are not very close in the actual play.
In Act I Scene i, Romeo's mother and father, Lord and Lady Montague, indicate to Benvolio that they are worried about him, but they don't talk to him directly (see 1st link, lines 111-151). They send Benvolio to find out why there son is depressed. This indicates that they care for him, but that they don't have a close enough relationship that he would open up to them.
For the rest of the play, they are absent entirely, until the very last scene. Even then, only Lord Montague is there because Lady Montague died of grief after Romeo was banished (2nd link, lines 221-223), showing that being without him tore her apart emotionally. Romeo leaves a letter with Balthasar for his father before he kills himself, which indicates that he cared for his parents and wanted to say good-bye (2nd link, lines 23-24 and line 297).