Re-wire Cat5e RJ11 jacks to RJ45 ethernet
I'm no pro, but I'd say you can do as you wish with low voltage cable
I'd guess the daisy chaining was a poor mans way of propagating the phone cable without running it back to the closet.
Yeah, see the last answer
I'd remove the phone jacks and short out two of the pairs with clip leads.  Then use a continuity tester to map out the cables.
Does the grey one lead to the attic somewhere?


I'd say you can terminate the cables you need with wall plates in the rooms, RJ45 jacks in the closet and if you need additional service to one of the daisy chained rooms, you can add a switch where needed to continue the chain.  Mount the switch to the wall close to the wall jacks to get it out of the way.