Evouchers work on a per segment basis (i.e. you on a EDI-FRA-HKG you have to upgrade each flight separately).

You need 2 evouchers to upgrade one way from C to F, or from Y to C (valid for all fares classes except S and W). If your reservation already has your LH number in it then you should be able to see it under "My bookings" on the website. If the flights are LH operated then you can actually confirm the upgrade online (just click on the upgrade link that appears when you call up the reservation online). Alternatively you can call LH and get upgraded in advance over the phone.

I always check by phone if I upgrade online. LH IT systems are a bit useless sometimes, as you are discovering!

The evouchers will be deducted automatically as you board the plane (though occasionally there are glitches and the vouchers get deducted ahead of time - this is fine as it will clearly show up on your account).

As to checking upgrade space, this is something I have only been able to check over the phone in recent times. There used to be ways of checking online but these have gone, and LH will not show upgrade class availability on travel agent CRS systems.