1. Contact the ISP and ask them if they know how the two networks are configured - sometimes they are asked to route between subnets or physical networks. If so, it might be best to ask for that to be abandoned so that you can 'flatten' your network structure and have your VoIP handsets placed onto 'Port 1'. Once on Port 1, and so long as the VoIP provider agrees (see 2), your handsets should get their IP from your DHCP server and you will be able to utilise the 'remote' network cables etc.
2. I would contact the VoIP provider and ask them to enable DHCP for the handsets (this is normally very easy to do centrally).
3. You don't 'need' VLANS for your network - but it's sometimes nice to get the extra security and other features it would afford. Keep it simple right now, though: flatten things, get your VoIP handsets assigned IPs with DHCP, and make sure you can use the whole network and its infrastructure. Tweak and secure later. Unmanaged switches aren't great for this, and that's probably why they opted to segregate the LAN using the Huawei router. They will need to spend some money for a managed switch with the required features if they want to utilise VLANs at a future date. Like I said, for now, make things easy on yourself...
4. I would do this over the coming half term (or better, the summer)!
Good luck!!!