Answering the first query. If you take a look at the RJ45 sockets, you will see one marked as EWAN (or something similar) and coloured red. It is to that socket that you would connect either a VDSL2 capable modem or a modem/router configured as a pure bridge . . . such as your Billion BiPAC 8800NL, for example.
As for the second query, if the scratch has cut (or otherwise damaged) the printed wiring tracks than you might as well just consider that device as dead and only fit for the electronics recycling pile.
My neighbour used to use a Huawei HG612 as the VDSL2 modem and a BT HH3 as the router/firewall/DNS server/DHCP server/WiFi access point. So yes, what you would like to do is feasible . . . but maybe not with your damaged BT HH3.