What the 560 V / 7.6 A rating means for your power stage
The SPA08N50C3XK: That 560 V rating puts it solidly in the 500 V–600 V class for off-line AC-DC converters, power-factor-correction stages, and flyback or LLC resonant topologies where the DC bus sits around 400 V. The 7.6 A figure is at Tc = 25 °C — in a real enclosure at 85 °C ambient you will derate that number, and the 32 W package limit is the ceiling to watch when sizing the heatsink.
600 mΩ Rds(on) — conduction loss and gate drive
That 10 V drive level is the recommended operating point — the part is not characterised for logic-level gate thresholds. The maximum gate threshold voltage is 3.9 V at 350 µA, so a 5 V logic output will barely turn it on; you need a proper gate driver that swings to 10 V to get the rated Rds(on).
TO-220 Full Pack — mounting and thermal interface
The PG-TO220-3-111 full-pack package has the backside tab fully encapsulated in moulding compound, so the tab is electrically isolated from the drain. That saves you an insulating pad and washer when bolting to a grounded heatsink — just apply thermal grease and torque it down.
Infineon lists the SPA08N50C3XK as Active.