I am a portrait photographer and am wondering do I need a permit to take phpros of a client ?

I do not think that you need a permit for taking the photos.

Not that I know of, I use to do a little photog and have shot there a few time with clients and didn't need them.

I don't think that you need to take.My friend did the same for his client.

Not to my knowledge unless you are trying to secure exclusivity at a location or field in the park.