I assume that your USB socket / voltmeter is something like this:-**broken link removed**
That will have a converter to convert voltages around 12 V to 5 V. When the battery voltage is down to 8 V, you have taken all the useful energy from the battery. That is too far and you risk damaging the battery. If it does get that low, charge it as soon as possible. Even at 11 V, you have taken nearly all the energy from the battery.
At 8 V, the converter that converts around 12 V to 5 V will have stopped working correctly, and the 5 V will have started to drop. That is why the phone won't charge. There isn't much you can do about that, and anyhow all the energy in the battery has been used up.
The sockets are 5 V, 1 A and 5 V, 2.1 A (Not Ah). The 1 A and 2.1 A are simply the maximum current that the sockets are rated to. With USB, it is more complicated as the data pins are used so that the phone etc can work out what type of socket it is connected to.
A 12 V, 7 Ah battery should be able to supply 1 Amp for 7 hours, or 0.1 A for 70 hours. It will probably be less than calculated at higher currents, and more at lower currents.
The 12 V to 5 V converter, if it were perfectly efficient, would produce the same power out as it takes in, so if you had a 1 A load at 5 V, that would be 5 W so it would need 0.417 A from the battery, and that should give you 16.8 hours running from the battery.
Of course, the converter won't be perfectly efficient, and both the voltmeter and the converter are likely to take some current whether there is a load or not, so both of these things will reduce the life. Certainly leaving the voltmeter and converter connected when the sockets aren't in use isn't a good idea. On the other hand, when you are charging a phone, it won't take the full current for the whole time.
Another way of looking at it is that the lead-acid battery is rated at 84 Wh (Watt hours) and a mobile phone battery is rated at around 6 to 8 Wh, so you should be able to charge a phone 10 times, but say 5 or 6 to allow for the losses.