the airport is configured as Bridge (not DHCP), because I connected it with my fastweb router.
Check the Model No of the AirPort Express on side of the device. A 1st Gen AirPort Express is Model No A1264.
Apple started using the "Generation" naming with the introducting of wireless "n" products. Chances are, you have a Model No A1084 or A1088 which are older versions of the AirPort Express that do not support "n" wireless.
You need a Model No A1264 or the newer AirPort Express, Model No A1392 if you want to extend the Time Capsule's network wirelessly.
1 - Our Time Capsule is version 7.6.4, should I replace it now while I'm updating everything else?
Unless you simply want a new product, there would be no reason to replace the Time Capsule that you have now....unless you have recently purchased a MacBook Air laptop, and want to take advantage of faster wireless speeds.
However, even if you purchased a new Time Capsule, your current wireless devices will operate at the same speeds that they did before.
2 - If I replace my existing Time Capsule, can I transfer my back-up files to the new Time Capule?
Yes you can, but this is a complex procedure. It would be much simpler to start with new backups on the new Time Capsule and hold onto the old Time Capsule. Chances are after a few months, you really won't need all the old backups on the old Time Capsule, so you can erase the drive and use it as a spare drive or sell the device.
3 - Should I replace the AirPort Express we are using to connect to the stereo with a new version so that AirPort Utility supports it?
That would be a wise investment.