Почему не принимается "He has come on time."?
Скорее всего потому, что есть точное указание времени — вовремя, и должен быть Past Simple.
Can you use прийти/приходить for the sexual meaning of "to come", too?
No. We have a different word with that double meaning - кончить ("to finish"). Note that other variations of it ("закончить", "окончить") don't have sexual connotations and as a result are used more often in normal speech.
and what would be this verb's perfective form?
It is perfective (the imperfective one is конча́ть).
why does prishle pronounces like ;rishlo with an O, not an A and for sure not an E
It's “пришёл.” That e with the umlaut is read “yaw” in Russian. I thunk it's written “prishyol” in Latin alphabet.
Are these newly formed verbs perfectives?
Is this correct also?: "He arrived on time."