
I really don't get the whole alpha and omega things. Can someone please explain?

Explanation guide here http://puppylover857.deviantart.com/journal/Omegaverse-Explanation-and-Guide-441250200

That guide is solid for understanding the alpha/beta/omega things, but is hit and miss in the details as some omegaverse's operate different than others depending on the mangaka (i.e. that guide doesn't mention bite-marks, which is surprising).
The mangaka gave a bit of detail on their version of their omegaverse on pages 9 and 10 of chapter 1, which you can find here:
http://www.mangago.zone/read-manga/kurui_naku_no_wa_boku_no_ban/mf/c001/9/

I love this Yaoi, its so intense. It is literally worth the wait for the new chapters, they always deliver excellence (≧∀≦) I think i might need to start it again, because i got quite confused at some point. Can anybody explain to me the whole situation with his dad again and also how he got the job as a yakuza bodyguard in the first place? please?

(I suppose you're talking about Doumeki)
Doumeki's family adopted a girl. The girl fell in love with her brother, so he decided to keep his distance. He became a cop, and then found out that his sister had been raped by their father while he was avoiding her. He beat the shit out of his father and to protect the family reputation didn't mention the rape part and had to go to prison.
When he got out he strated working in construction work, where a guy from a loan company (guess that's the name) saw him and asked him to work for their company because Doumeki's well-built. The company was yakuza so he kinda got dragged into all that. And Nanahara thought they could use him as a bodyguard because they were short on people, Yashiro got interested in him, saw he was impotent, and made him is driver and bodyguard.
There you have it ^^
(but just read it again)

ONLY CONTINUE READING IF YOU WANT TO KNOW WHAT HAPPENS AND HAVE NO INTENTION OF BUYING THE MANGA........................................................................................................................ He survives but is in critical condition for a while, constantly getting visits from his partner and the uke. Amidst all the critical condition he finds time to give the uke a hand job. When released from hospital he has more sex with the uke while bandaged. Dropping his partner off one day, he's about to drive off but sees the killer across the street, through peripheral vision. Shouts out to his partner to watch out, the guy with the long wavy hair gets shot in the head by the killer and dies. The uke recieves a call from the killer and walks directly into a trap and is kidnapped and raped at gun point and with a gun. There's a shoot out between the killer and the police investigator, which ends with the investigator putting a knife through the gun man's right hand and holding a gun to his head about to kill him. The uke shout for him to not do it, so the seme lowers his gun, goes to the uke and removes the gun the killer shoved in the uke's ass. They have a lovey dovey moment, until the killer gets free and tried to stab the seme in the face with the knife that's wedged through his own palm. The semi's face gets sliced on the cheek, separating him from the uke. The killer grabs the uke and after verbal confrontation between them, the seme shoots him right through the head. Then the seme and uke are home having sex happy ending-ly.

THE PARTNER DIED?!?!?!?! WHAT NOOOOOOO YYYY WTFFFFF QQ
I've just started this Manga and i'm quite confused. i really don't mind spoilers, but can someone please just tell me the premise? What's the whole clan thing? Is Amano Kou the protagonist? What happened 9 years ago? And will him and Touya be allies?
And who is the guy in this chapter? http://www.mangago.zone/read-manga/genwaku_no_kodou/mf/v02/c006/41/
amano kou is the main protagonist. touya is his closest ally. although the beginning is a bit confusing, everything becomes much clearer later on. so you will find out more about the clan business, what happened 9 years ago, and who that guy is as you read on.
Thank you !!