You can find all Takumar lenes here: http://kajiwara.weebly.com/index-et-prix-des-takumar.html
It´s in french, but as you can see there is one Super-Multi-Coated Takumar-zoom 85-210 f4,5

70-200 f 2,8 is not a rebranded Tamron, it is made by Pentax, and Jun Hirakawa, who is a former legendary lensdesigner at Pentax and has for example designed Pentax 85mm f 1,4 and the two limiteds
43mm and 77mm and several others Pentax lenses, is now working for Tamron. He knows Pentax very well and I suppose that is why Pentax rebrands some of Tamron´s lenses

For me, five min is more than enough, but I can understand that there are people that want longer exposuretime

The limitation is about 5 min, it depends a little of the lens, time of year and your place.

Pentax K1 has GPS and something called "astrotracer" which means that the sensor moves, follows the stars. How much it moves depends of the lens you are using and where on earth you are.