Did you mean the Airport Express will always need to be connected via ethernet.
I tried to make this clear when I said that.....
you will need to plan to connect the Express to the BT Home Hub using an Ethernet cable.....which must be connected at all times. The Ethernet cable can be virtually any length that you want.
So, to clarify......connected at all times would mean that the Expess will always need remain connected to the Home Hub this way. In other words, the Ethernet cable cannot be disconnected, if you want the AirPort Express to perform correctly.
IF.....you had another Apple router set up as your "main" router......instead of the Home Hub.....then, the AirPort Express could be configured to connect to the "main" AirPort wirelessly. In other words, to extend a network wirelessly, you always need two Apple routers.
I was hoping to put it in the middle of the house 3 rooms away from the Home Hub to extend the network.
I also noted that the Ethernet cable can be virtually any length that you need, so 3 rooms would not be a problem as far as length. Ethernet cabling can be run 300+ feet, or about 100 meters with no signal loss.
If you cannot run the Ethernet cable, then you might be able to use a pair of Ethernet Over Powerline (EOP) adapters to send the Ethernet signal over the existing AC powerlines in your home. The theory with these devices is that you already have the wiring in place....you just need the adapters. In practice, things do not always work as well as the theory suggests, so if you decide to try a pair, it would be a good idea to understand the store's return policies in advance.
Any computer / electronics superstore will have a selection of EOP products, which are sometimes called Homeplug adapters as well. Ask the sales person there to recommend a brand that works well in your area.
When you have a good Ethernet connect established between the AirPort and the Home Hub, then we can work on gettting the AirPort to display a green light, which is what you want.
As far as Yosemite, you should update your Mac to the current version, which is 10.10.5, since there are some improvements and fixes in there.