Can I repurpose this RJ45 setup for phone to run as Ethernet?
For the last couple of decades, many new homes have been wired using UTP cabling because its not significantly more expensive than plain old phone cabling.  

So its not uncommon for cat5 and cat6 cable to have only one pair used for a `phone, and the other pairs idle.   It will be relatively straightforward to reterminate both ends of each wire.

At the room end, you will need a new faceplate and a new jack for each wire.  One jack per cable is correct - ethernet can't be daisy chained like a phone.


  There's some cost saving putting a cat5 jack on cat6 wiring, but there's literally no gain putting a cat6 jack on cat5 wires.


At the central point, there should be one run of cable to each remote room.  If you don't have this, then someone's done daisy chaining and you need to investigate further.

The wires in the walls should be Solid Core.  While it is possible to get plugs for this, the normal best-practice is to terminate the solid core wiring on a patch panel, something like this :



And then to run short stranded patch cords into your switch or router.

Tools: Crimp for plugs, punch-down tool for jacks, a cable stripper for ethernet.  Optionally a tone source tool can help with discovery, and a cheap link tester helps show if any of the individual wires are broken.  And the usual screwdrivers etc.

Consumables: wall plates, jacks, one patch panel(the most expensive item), a short stranded patch cable per link, a longer stranded patch cable for use in the remote rooms.

You also need to think how your router can connect to this switch.  Its possible to use one link to backfeed the LAN through to a switch at the central point.  It may work for you to move the router into the central point, though this can cause issues with wireless ethernet signal strength. 

This is all a bit generic, but we can be more specific as you provide more details.