Well, these are your questions, with answers (of my understanding and experience).

1. I'd like what is the reason for this kind of interaction?

Answer: I am not sure that whether another cat was trying to jump over him to attack, or that was actually the female cat. Cats make noise while doing Sex. And also they Meowww while fighting. but the voice while doing Sex is a bit different and irritating (for humans). And if that was very first time for your cat at home yard, then it would be probably sign of attacking or fighting with other cats.

2. Is it better to let him go outside (any time in the day or in some specific times)?

Answer: There is nothing wrong in allowing your cat to go outside, or letting them go to home yards. You should go with him to show him the streets and paths few times, as he must be aware of the way (back to home). and it would be more secure and safe to keep your cat at home at night. and allow him to go out at day time. But keep one thing in your mind that when indoor cat is allowed to go out, then there are also some wild cats there (Outdoor cats), some of them are always ready to fight and attack. so, you may face some injuries of your cat (as it is normal condition, if there are such cats). and also you are having the male Persian cat, therefore it is in the nature of male cats (outdoor), that they don't bear another male cat in their area MOSTLY.

3. Is it possible my cat (boy) could find a girlfriend by himself in this contact, if yes, what months are better?

Answer: Most often, the male Persian cat is sexually matured at the age of 7-12 months. so, it is also possible that your cat has got or found its partner.

Don't forget to vote-up or consider this answer as Correct, if you got accurate answers.

Here is my understanding and experience of your questions.

1. I'd like what is the reason for this kind of interaction?

Answer: I am not sure that whether another cat was trying to jump over him to attack, or that was actually the female cat. Cats make noise while mating. They also meow while fighting, but the voice while mating is a bit different and irritating (for humans). And if that was very first time for your cat at home yard, then it would probably be a sign of attacking or fighting with other cats.

2. Is it better to let him go outside (any time in the day or in some specific times)?

Answer: There is nothing wrong in allowing your cat to go outside, or letting them go to home yards. You should go with him to show him the streets and paths few times, as he must be aware of the way back home. And it would be more secure and safe to keep your cat at home at night, and allow him to go out at day time. But keep one thing in your mind that when indoor cat is allowed to go out, then there are also some wild cats there, some of them are always ready to fight and attack. So, you may face some injuries of your cat (as it is normal condition, if there are such cats). and also you are having the male Persian cat, therefore it is in the nature of male cats (outdoor), that they generally don't tolerate another male cat in their area.

3. Is it possible my cat (boy) could find a girlfriend by himself in this contact, if yes, what months are better?

Answer: Most often, the male Persian cat is sexually matured at the age of 7-12 months. So, it is also possible that your cat has got or found its partner.