Of course. Not sure where its sold though. Im sure you can get whatever length you require from a well known auction site if you cant find any on the high street.
If wireless or powerline adapters are not an option for you then the best option would be to run a lengh of CAT6 cable from your house to the garage, that way you can have a wired connection and always place a wireless connection on the end of it if you need wireless in that area.
Infinity needs to be connected to the master socket and you can only have one master socket.
The Homehub you will be given will be the Homehub 5 which has an integrated modem. If you tried connecting it to the garage telephone extension and use a micro filter it might work but you would need to get another HH5. You may also have problems with DLM if you are switching home hubs off and on.
A better option might be to run Ethernet cable to the garage and connect a separate router such as TP-Link TL-WR702n wireless N router/range extender which simply connects to the Ethernet cable and will give you a wireless network in your garage. You will not need to switch off the Homehub for it to work.