Use 2x5V from USB ports to speed up device battery charging? Do we get enough current (1A) from this 2 USB ports as well as from AC charger? I assume that voltages need to be the same, but what'll happen if they are not?
Supplying a device from two USB ports (but at one PC) is very common with a Y cable:
You have some idealized view to the modern products, in our reality:
rare mainboard implements current limiting capabilities (beginning from the design); and
yet rare mainboard uses such capabilities even it implements them.
Typical mainboard has a simple PTC resettable fuse in series of the VBUS circuit. Frequently, one fuse is used to protect two ports, e.g. in a backpanel 2xUSB+something jack. Therefore, the greed degree of a device is a good will of that device. An intelligent charger may limit itself if it fails to negotiate with the host, but again, rare host can intelligently limit it.
Also, a non-charging USB 3.0 socket should solely provide 0.9 A and is backward compatible with same type USB 2.0 plug.
To charge faster it is preferred to use a shorer cable and/or a cable whose power pair has a larger square resulting in lesser resistance in series between the power source and the burden.
Relating to your scenario, of course, not in all possible cases, the different voltage problem exists only with supplying from two different sources (supplies) and the only right way to solve the problem is to avoid such connections for power feeding.