Current consumption and UART speed on MKRZero.

I noticed the tech spec says 600mA at 5V, will it have problem with normal USB 2.0 which supply only 500mA?

For the UART with uno and nano I was able to reach 2Mbps with processing, can I get the same speed with MKRZero?

Both the UNO and NANO use a very much slower processor.
Its not unreasonable to expect a much better response from the SAMD.

You haven't included any detail as to what was connected to the other boards and how.
The specs for the SAMD21 are here.

Compared to the 16 Mhz used by the other boards and the better arithmetic functions inc UART differences you should be fine.

It will not have any issue running on the 500mA USB ports Just don't load up all the pins with extras that may be current hungry and if you do consider supplying those items with thier own voltage and just a common ground to the Arduino.