But Im still wondering, can a UPS, equiped with a (i.e.) 13.0 V. 7.0 amperes/hour Lead Acid batteries, charge and use an automotive 12V, 60 ah/hour Lead acid? And should automotive batteries be moving and shaking periodically? I mean, not to be used as stationary Battery.
A mentioned before, use a deep cycle battery which is the same type used in RVs, boats, and solar systems. Your UPS will take a long time to charge the 60Ah battery (10x as long as the little battery) so it won't work if the system is on UPS a lot and doesn't get time enough to recover between power outages. You could add an external charger which will dominate the internal one of the UPS. And no, the batteries don't have to "move" and "shake" at all.