It depends, you can use ethernet cables (the higher the category the better the quality) in your flat even for the analog part between first face-plate and modem (you simply use a single pair).
Not a bad idea, currently that would probably mean to use cat6A, cat7 or cat8, but for the short runs typical all of these should work for >= 10 Gbps ethernet.
That would likely be coaxial cable, which is not useful for normal ethernet (I think with 10o Mbps FastEthernet twisted pair cables became mandatory). There are adapters (MOCA) to use coaxial cables for ethernet, but I would not recommend those unless for specific issues (like an existing coaxial cable between two locations that is hard to replace for whatever reason).
I said "likely" for a reason, I can not figure this out from my side conclusively, but the overview/diagnostics/information page of your modem might contain information to answer that question.
Generally it results in higher SNR to disconnect everything but the first face-plate and connect the modem there, and connect phones only to the router VoIP-basestation, but that requires your ISP to actually use/allow VoIP/SIP and not analog POTS.
As far as I have heard in the UK (I assume you are in the UK) most ISPs will accept users switching between PPPoA and PPPoE (assuming an ATM/AAL5 carrier to begin with, on a PTM link PPPoA is NOT an option anyway).