The peeing is self defense- it is supposed to taste bad and can cause irritation if you get it in the eyes. (Note- I have no first hand knowledge of this as my general procedure has always been to neither taste pee nor to put it in my eyes).

I'm also fairly convinced that part of their self defense when picked up is to stick to you like the Millennium Falcon on a star destroyer until they have a good chance to escape. This is based on the many, many wild ones that I've handled to move out of danger (i.e. the lawn mower, whipper snipper, top of a closing door, etc). Once picked up, they tend to stick to you like glue, tame or wild, and I've walked around with wild Grays on my shoulder.

They will eventually get used to some handling, I do usually take my grays out of their tank when I feed them mealworms or waxworms (a couple of times a month) and they don't generally pee on me anymore (worm feeding time is also usually photo shoot time or cage maintenance time). Take it slow, and don't force the handling. Remember you should have her for many years to come so you've got lots of time to get familiar