A geas--that's Celtic--is a word for a oath or a spell of compulsion, it's used a lot in Celtic myths and legends.  In this case, the Titania places it upon her messengers to ensure that they cannot lie, a useful trait in a messenger.  A geas could sometimes be used as a punishment, in one of the Celtic myths, the King of Ireland's High Druid placed a geas upon a proud warrior to humble him and made him thank everyone who did him a favor for a year, including people like servants and slaves, and do them a favor in return. 

As for the last one, Severus did tell Harry he could write to his friends and he assumed he would tell them of his newly discovered relationship, he really didn't want Dumbeldore knowing just then, because he wanted to find out the old man's motives.  He doesn't know about Sirius yet, so he might be a little ticked off when he finds out, but otherwise he understands Harry's need to share this revelation with Ron and Hermione.