At the end of the specifications there is the function [Report incorrect data] for this.
This should be more appropriate than "a question about the product".
Yes, that works. You can connect the 10 Gbit port of the Fritzbox 5690 XGS to the TP-Link TL-SX105. The switch then distributes 10 Gbit/s to all devices, provided that they themselves support 10 Gbit and you use suitable network cables (at least CAT6a).
I was able to do some research and according to the manufacturer, this model has 5x 10G ports:
5× 100Mbps/1Gbps/2.5Gbps/5Gbps/10Gbps ports, auto-negotiation, auto-MDI/MDIX
What you have planned is therefore entirely possible. For example, you can have a 10G connection at one end of the cable and a 2.5G at the other. The throughput would then be 2.5G.
Yes, each port is a 10Gbit Ethernet port. Internally it has up to 100 Gbps of switching capacity, so it should be possible. Also it doesn't use any fans, so it's completely silent.
With a 10 gb router and a cat 7 cat 8 cable you can use both only the question is if your devices are 10gb capable i have a 10gb modem with a cat 3 cable but since my playstation only needs 1gb i can't give it more than it needs hence a cat 3 cable i hope was helpful