1. I doubt the BT engineer will be concerned with tweaking the connection to your preferences. He is there to do the install, connect up the line, make sure it is working and that the router supplied functions OK. Anything beyond that would be up to the end user to tweak for themselves.
2. HH3 supports b / g / draft n but not n 5Ghz.
BT Home Hub 3 specifications | Expert Reviews
3. The BT engineer will do the install using the supplied router. If you want to change it back after thats up to you. Just remember you will need to phone support to get your username and password as the BT HH3 connects automatically.
4. The HH3 comes with standard facilities on it. At home there is little or no req for you to be using static ip addressing. It is more sensible,and efficient from an end user's point of view, to allow the devices to pick up an address from DHCP then on the router tie the MAC address of the device to that ip address ensuring it gets dealt the same ip everytime but without the hassles of manually configuring each device.
5. If you mean on your LAN then answered above. If you mean a Static IP address for your external address on the router then I think you need to speak to BT but I think it means getting a business BB connection rather than a residential.