Can an equipment built for 220V/1ph/60 Hz be connected to a 208V/3 ph/60Hz grid by using only two lines of the 110V each across the load?
A line and neutral of a 208-volt distribution system will provide 120 volts. That is only a bit more than half of the needed 220 volts. Any 220-volt load will operate very poorly or not at all. If you can get two 120-volt hot lines from a 208-volt system, you will have 208 volts. That would probably provide reasonably acceptable operation for many 220-volt items and even the more common 230-volt equipment.
3 phase, 208 volts has a phase voltage (line to neutral) of 120 volts AC and not 110 volts. If you applied 110 volts there is no guarantee that the equipment (unspecified) will work under all reasonable circumstances.
Yes, but 208V/3ph would not have a 110V phase voltage. You have to be careful.