It was a bit on the desperate side, but after all, this is a tragedy so something has do go wrong.
He is supposed to hear it from Balthazar, but Friar Lawrence doesn't tell Balthazar, but sends the message with Friar John instead. As a result, Romeo never learns of Friar Lawrence's plan.
The timing of Friar Laurence's plan was affected by Lord Capulet's decision to move the date of the wedding.
Friar Lawrence sends a letter to Romeo, who is in Mantua, detailing his plan to fake the death of Juliet, and have Romeo bring her to Mantua where they can both live happily ever after. He gives the letter to Friar John, who is supposed to bring the letter to Romeo ASAP. Friar John never makes it to Romeo, because he was quarantined due to an outbreak of the Plague. Therefore, he brought the letter back to Friar Lawrence. This messed up Friar Lawrence' plan, as he had already set it in motion.
Juliet and Friar Lawrence made the plan to fake Juliet's death so she could runaway with Romeo. They had planed for her to take a vile that would make her cold and fall asleep for 48 hours. Friar Lawrence sent a note to Romeo telling of their plan so Romeo and Friar Lawrence could go retrieve Juliet once her funeral was over.
She is confused and desperate because she does not know what to do and was going to kill herself if Friar Lawrence did not come up with a plan to help her.
Friar Lawrence's plan went wrong when the message he sent to Romeo informing him of Juliet's fake death did not reach him in time. This miscommunication led to Romeo believing Juliet was truly dead, causing him to take his own life. Ultimately, Friar Lawrence's plan failed due to poor timing and unforeseen circumstances.
By a horse :D
The plan is that his brother Friar, Friar John, will take a letter to Romeo. But Friar John is prevented from giving him the message.
She was anxious and desperate. If the Friar had not thought of a plan her intent was to kill herself, right there.
Friar Lawrence organises for Friar John to bring Romeo news of Friar Lawrence and Juliets plan (Act Five, Scene 1)
Juliet meets Friar Lawrence at his cell, where they form a plan to fake her death using a potion that will make her appear lifeless. She hopes to avoid marrying Paris and reunite with Romeo.
Juliet threat to kill her self