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31a Compensate district court with time rather than money ultimately (10).
Looks like 'counteract' but I can't parse it.

55a Perverted server of queen seduced by Zeus? (3,6).
Looks like 'led astray' but I don't understand any of that server of queen and Zeus stuff.

48d Angry with fivefold increase initially in rubbish (5)
Dross?

48 It's just the usual Roman numerals - Cross, angry, gets the C swapped for the D (fivefold, 100 becomes 500) for Dross,rubbish.

55 Led Astray, perverted. Leda's queen seduced by Zeus , Tray, server.

31a COUNTERACT = COUNTY + CT, then ERA replaces Y

Thank you. 'Leda' is new to me.

40d Striking skill involved with boring pastime (9) f?n?s?i?g
Finishing? Finessing?

Looks like f(in)ishing

in = "involved with"
"boring" = inclusion indicator
fishing = "pastime"