Juliet refused to go.
because he thinks he hears the capulets coming from outside and wants to escape before they find him
Friar Lawrence's plan at the end of Act 3, Scene 3 in "Romeo and Juliet" is for Romeo to spend the night with Juliet and then leave for Mantua in the morning. The Friar hopes this will allow Romeo and Juliet to eventually be reunited and that their marriage will bring an end to the feud between the Capulets and Montagues.
they say she must marry or move out.
Friar Lawrence tells Juliet that Romeo is dead and urges her to leave with him to a convent, where she can live in peace and mourn in safety. He reassures her that he will help her and that things will eventually get better.
She says no, but then the friar is afraid of the watchman that is coming. the friar then leaves without Juliet. When the friar left Juliet finds the poison bottle and is upset that Romeo didn't even leave a drop for her. She then kisses his lips hoping there is poison still lingering on them. She then finds his dagger and stabs herself in her chest. She then dies in Romeo's arms.
Friar Laurence advices moderation in love, not violent excess. Then Romeo, Juliet and Friar Laurence leave to get married.
Romeo doesn't receive Friar Lawrence's messages about the plan because the messenger he sends, Friar John, gets held up due to a quarantine in Mantua. As a result, Romeo remains unaware of the plan and believes Juliet is actually dead, leading to tragic consequences.
The excuse Juliet uses is that she is going to Friar Laurence's cell for shrift or confession.
Friar Lawrence went to the tomb to get Juliet out of there because she was about to wake up and he did not want to leave her awake, surrounded by corpses. He was going to bring her to his cell until Romeo can come and get her.
Friar Laurence tries to convince Juliet to leave with him after she sees Romeo's dead corpse because they hear someone approaching the grave (most likely the prince and police). However, Juliet refuses, so Friar Laurence flees.
This really depends on your own opinion. Personally I believe that they shouldn't feel very guilty as they were only helping Romeo and Juliet with the choices they made. The Nurse even stopped supporting Juliet after Romeo was banished and suggested she should marry Paris, although this did mean Juliet was left alone. Friar Lawrence advised both of them before he married them that it was moving along to fast and he shouldn't feel guilty about Juliet's death since he did arrive in time to save her and he did try to convince her to leave the tomb with him and even if he didn't try very hard, Juliet still made the decision to end her own life.
Juliet decides to go to Friar Laurence's cell to see if he has a solution. She also decides she will never tell the nurse true feelings she has because she fears betrayel. If there is no solution , she will kill herself.