Can gums bleed when using a Waterpick for the first time?

Maybe for the first few times. When you start using one your gums are usually inflamed and not used to this kind of action.  They can bleed with water pick use at first because the gums will be soft, but after several goes the gums will harden up and be less susceptible. 

Yes they can. 

The trick is to not aim at the gums, but the teeth and all the crevices. Normally no they do not bleed not enough pressure, this isn't a power washer.