because the player is new, although we had a great connection, and I don't remember any crashes happening to me or my opponents during the game,

I want to tell you that I've been playing Heroes for quite a while, although I've mostly played in LAN mode, and crashes happen quite often, and not just disconnections, but also just "hangs."
And it was very inappropriate of you to speak in such a tone, especially to someone you don't know. For me, such statements are offensive. I never even thought of anything like that. It seems like you have a single policy here and a lack of trust in each other. Honestly, it's disgusting.

his long turns were also suspicious

What else made you suspicious?

that we are playing fairly and I believe that everyone has the right to demand fair play from their opponent...

Please answer the question I asked:

Yes, by the way, what right did you have to recruit 28 fairies when it's forbidden? And after that, you'll say you're playing fairly?

FORBIDDEN:

to attack an opponent within the first 8 days

to attack on the first day of the week with a creature born on that day

to choose: Sir Mullich, Adel, Roland, Solmyr, Kira, Aislinn, Tant, Isra, Vidomina, Alamar, Zhedit, Deemyr. If these heroes come to you in the game, you can only use them until their level increases by 2 compared to what it was at the time of acquisition. Upon reaching this limit, you must remove the hero before the end of your turn.

to sell artifacts for more than their actual value.

to recruit neutral units, to dig for the Grail

I demand that the organizer react to this violation. Below are the saves that prove it. 28 fairies is not a lot, but - firstly, it's good for clearing out the early days of the game, secondly, it contradicts the rules, and thirdly, I wouldn't have brought it up if I hadn't been accused of unfair play. The most interesting thing is that before the game, my opponent reminded me that we were playing without the Grail and without recruiting.