Good news, guys!
Thanks everyone for help one more time!
So, I received first ordered item - IRF7404 Mosfet P-Channel 20V 6.7A. Yes, I understand that 20V is too close to 18, and I will replace this Mosfet after I will receive the recommended one. I just wanted to test without full load, and I assumed it should work. And it did!
Now, I can switch on my machine and everything seems to be working, except, of course, one bottom motor, which I didn't connect.
What I've noticed is that in this circuit for the bottom motor - something is heating very fast, in one second after switching on. It seems like this part, that I circled on the photo. What might it be? Do you think it is because of the burned components in this circuit? Don't want to have new components to burn again.