Can I, owning a router (well, or a router), manage the connections of other users to it?

Question

Computer networks

Connection management refers to the ability to change the connection speed of a particular user (increase/decrease)?

Answer 1

Yes, you can, if the software of this instance allows you to implement these functions.
Mikrotik for example.

Answer 2

You can, even if you own a switchboard. If this is an L2 / L3 switch or with QoS and ToS support, you can quite control the prioritization of this or that traffic.