300 Amps if used for service entrance conductors. Table 310.15
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It would be at least 250 amps, maybe 300 amps.
4/0 (4 ought) in copper will handle 250 amps. The voltage drop at 175 ft. is about 2.14 volts which should be okay.
There are two distinct questions here. To determine the wire size to carry 15000 volts the circuits load amperage must be stated. The wire size for a 550 amp service is, an 800 MCM copper conductor with an insulation factor of 90 degrees C. This conductor is rated at 555 amps. Parallel 250 MCM will give you a total capacity of 580 amps. A triple run of 2/0 will give you a total capacity of 585 amps.
A transformer is a power source. It will provide voltage to a device. Find the voltage rating on the device, say 24V. 250/24 = ~10A.
Yes, this is a safe connection. A range is usually wire rated at 40 amps and the manufactures do not make a 40 amp rated receptacle. The code requires the next highest rated receptacle be used which is a 50 amp rating. This is why the range receptacle is rated at 50 amps. This receptacle is known as a 3 pole 4 wire grounding receptacle, 14-50R 125/250 volt. Black wire to terminal X, red wire to terminal Y, white wire to terminal W and ground wire to terminal G.