Yeah, what IS with those two?! Friar Laurance's actions range from rash to strange to downright immoral, while Lady Capulet seems at times like the worst mother since Cinderella's stepmom.
Let's start with Friar Laurence. He is, of course, a monk, but his responsibilities are more like those of a present-day priest. In medieval Verona, wealthy families had their own friars, who performed all the services and rites of the church for them. Thus, it is natural for Romeo to go to Friar Laurence when he wants to wed Juliet.
It seems strange that Friar Laurence agrees to Romeo's hasty request so quickly until we realize his motive. He says in Act II, Scene III, that he will perform the wedding in the hope it will force the two feuding families to stop fighting. This seems like a lofty goal, and we can sort of believe it might work (for a while).
The friar's plan for Juliet to drink a potion that will make her seem dead, send a letter to Romeo, meet them in the tomb, etc., however, is truly wacky. It requires the audience to not only suspend its disbelief, but break with sanity. Shakespeare uses this fantastical device more as a way to show the frailty of human plans in the face of fate, which has doomed the star-crossed lovers from the start, or at least from the prologue. In this case, fate takes the form of the plague when the messenger, Friar John, is prevented from reaching Romeo in Mantua because he has visited a quarantined house. And we know what this random act of fate sets in motion.
Lady Capulet is somewhat more believable in the context of the time. Noble families had little involvement in raising their own children, instead farming them out to wet nurses as infants and marrying them off young and hopefully well. Lady Capulet's (and her husband's) insistence that Juliet marry Paris would have been quite normal; we learn that Lady Capulet herself was wedded and gave birth to Juliet quite young.