You can use an RJ-11 in an RJ-45 and have it work correctly. We've done it numerous times here where I work. If you use standard wiring (A or B) on the RJ-45 keystone, your middle two wires will be the blue pair. With an RJ-11 plugged into the socket, the blue pair will match up with the red/green pair of the phone wire once you've plugged the RJ-11 into the center of the RJ-45.
Then it's a matter of what the other end of that network cable connects to to make it all work.
We have some special BIX blocks that also have RJ-45 connectors which are very handy for changing over from a network connection to a phone.
Also, for 1000 Mbps, you use all 8 wires, it's only for 10/100 Mbps that you only use 4.
Yes you should be able to get RJ-45 "keystone" connectors and punch the Cat5 cable onto it.
You will however need to punch the other end of the cables either onto a patch panel (recommended) or onto RJ-45 connectors. Then, those will have to be plugged into a switch which connects to your internet so that you have internet access for the VoIP phones.
Typical setup would look as follows:
Highspeed Modem >> SOHO Router >> Switch >> Clients (PC's, VoIP phones etc)
Your patch panel should be near your SOHO router and switch (which ideally should also be very close together and connected with a crossover cable) so you can jumper from patch panel to switch.
When it comes to network cabling, you will want to test all cables once you're finished to make sure they work properly. Those cheap "blinking light" testers are useless. I would recommend calling a company that installs network cabling and asking them how much they would charge you to test/certify "X" number of cables. In fact, I would call around and get quotes from several and go with the best price.