Amphenol is one of the top coax suppliers, stick with them if you can.
The Amphenol Global Search page, below, that has several entries that
my old computer can not talk to is VERY slow to respond. Hopefully you can get more information from them.
INSERT: Just found TFC-10;
created by(?): Times Fiber Communications
http://www.timesfiber.com
also made by Amphenol: https://www.amphenol.com/gsearch/ctfc-t10?page=1
The cable you have is 75 Ohm and has a shield layer that is extruded Aluminum, not foil like the indoor ones most folks are used to. As such it is probably a little more sensitive to repeated bending. If outdoors (as it is designed for) it probably should be restrained from flapping in the wind, repeated bending may eventually crack the shield, causing signal loss. (the flapping and bending is speculation on my part, based on the descriptions on the manufacturers website)
One site says you can directly connect RG6 to the TFC-T10 with an 'F' male-male connector. Since they are both 75 Ohm you should be good to go.
The amplifier you are looking for would be an "Antenna Booster" or a "Distribution Amplifier." Both require power and actually amplify the signal. If you see some that advertise improvement but do NOT require power, they are probably lying.
The Antenna Booster would be the lower cost option and would likely help/hide the problem.
Distribution Amplifiers come in a wide range of capabilities and costs, from \$$ to \$$\$$\$.
Cheers,
Tom