I am unsure if these options are not present on your router, but the following will be addressed:
Part I: can monitor which devices are connected to my router
You should be able to do this via the webpage interface (something like http://192.168.0.1) where you can create an access list. Simply enable this list and then add the mac address of the devices you want. Most newer devices will allow you to tick the current connected devices.
If you want to get your hands dirty, you could use something line nMap. This would be a more manual task to perform however. I will make the assumption you do not want to spend money on performing this.
Try GlassWire Free for monitoring this. This tool comes with a paid version with more features. I believe this is probably your best solution.
Part II: limit/adjust the bandwidth of a connected device
You can find a great answer to this right here: Limit Bandwidth. Pay close attention to the comment from @Hopelesssn00b:
"Alternately, as suggested by Andres, you can install
bandwidth-limiting programs on that PC, and depending on the OS and
environment you may be able to apply bandwidth limiting settings
natively. If it's a specific user causing this disruption, consider
using (or creating) acceptable network use policies to deal with it
The better option (in my opinion) would be to enable QoS to ensure the devices you want to get data first do. This is probably the most feasible option as I am unaware of software for iOS and Android to help.
A noteable mention would be to create muliple SSID's on the device to try and help limit who is on one connection, and try to maximise the performance of one SSID through QoS. Not sure of the feasibility of this.
Part III: ban an ip from being connected to my router
You probably cannot ban an IP because chances are you're using DHCP and not a Static IP. Again refer to point 1 where you can create an ACL to prevent devices from adding. You can attack this from two points:
- Configure this device on the ACL to be blocked by it's MAC Address or;
- Create a reservation on the modem for an IP and then statically assign this to the device.
Again, I would recommend creating an ACL on your modem. If you need any more help add a comment. If you feel I've answered this, please mark it so.