Plenty of manufacturers mix capacity in different strings.

The higher capacity batteries have a lower internal resistance (due to more plate surface area) and thus will discharge roughly their % of the load in relation to their % of capacity.

As hattix said above, so long as theyre not in series, its fine.

That's not how it works. You can parallel 12V lead acid batteries of the same state of charge. The main concern is not overcharging the batteries. After the bulk charge (around 14.5V), the voltage should be reduced to a float charge level (around 13.7V). Many battery chargers can do one or the other but don't switch to float when the battery is charged. Look for smart chargers which give their voltage specification for each mode.

edit: AGM gel and flooded batteries may have slightly different voltages. It is best to use a charger designed for the chemistry of the battery.

Voltage can't drop faster on the 7 because you can't have (much of) a potential difference across a conductor. The 7 Ah battery would need to be at a lower voltage than the 14 Ah battery and... well, how would that happen? In practice, the batteries are discharged in a rate proportional to their capacity, so the 14 Ah battery would provide 2/3rds of all current, and the 7 Ah would give 1/3rd.

If they're in parallel, the capacities will add and they'll always be at the same state of charge.

There are exceptions to this in extreme cases (where internal resistance becomes an issue) but I can't see you hauling over a hundred amps out of these things if all they are is a UPS.