What kind of consistency dose this "therapy putty" have is like the "thinking putty" or "gak" from nickelodeon?

There are actually 4 consistencies. The yellow one is like gak. The green one is a little bit more like thinking putty. The blue one is like if thinking putty was also weighted. Red is like a bit thicker gak. It's nice for kids because they can really feel out what they're wanting. A lot of the time it's more the green and blue because they are thicker but they like the pull of the yellow and red! Hope this helps!

it does say that it is made with silicone and not latex

Is there a weight associated with each putty? or a tensile strength?

Each putty container has a different tensile strength. The yellow is very easy to manipulate, the blue putty is much more difficult to manipulate. I bought this for my mother that had a stroke which affected her right side. She has worked up to the green putty. She has been using since February 2020.

Can this therapy putty be washed?

I don't know how you could wash putty, my recommendation would be to havecleane hands and use hand sanitizer before using, that is the practice at most therapy clinics