i dont get the unlocks from the story

This is not the problem, dude. 

I would know because I've replayed the mission several times, made all the choices, got all the achievements for those choices, collectibles, and difficulties, and have the screenshots to prove that there's a bug:

I've played several multiplayer matches, and waited more than 9 days but nothing. The assignments popped in-game, but the weapons weren't unlocked in multiplayer and the asignments still appear as locked both on battlelog and in the main menu.

I've deleted my campaign save data several times and did the assignments/campaign over and they unlocked and showed the weapon unlocking in-game during gameplay, but upon checking in the menu, the assignments were still locked. I've repeated this process several times hoping it would eventually work, to no avail. 

I spoke with the EA Support and they said "its a known issue and they're working on it to fix the problem" but didnt gave an ETA for when it might be fixed. This is despite the fact that EA/DICE tech teams have announced several times that they are no longer able to fix such issues in the Soldier Battlelog database system. Likewise, the EA User Support group does not have access to this anymore either, as BF4 support was outsourced few years back and the data access tools are not available to them at all. So they are probably just lying to our faces. 

 I've "unlocked" almost all the Dogtags and Weapons but they did not unlocked for me to use in Multiplayer. 

FIx your broken **bleep** game before continuing to sell it to people, otherwise you'll have a problem on your hands.