Does anyone know if I kill only first 4 in HC for example, will my loot in vault only be something from those bosses ive killed or do I get chance from all bosses in HC?
The Great Vault: Raid Objectives
There are three Great Vault objectives for raiding. These require defeating the Current Season Raid bosses each week. You can defeat bosses on any difficulty level; the rewards that are added to your Vault are from the loot tables of the difficulty that you complete. If you complete an objective in Raid Finder, expect Raid Finder loot. If you complete an objective in Mythic, expect Mythic loot.
So if I understand that text I will get a loot table from full HC, including the bosses that I dont kill
Yes, the loot you get is randomly picked from the entire raid loot table. You could kill the first two bosses and get the trinket from the final boss in the vault.
You can get later boss items if you’ve only done the first few… so it’s worth doing the first 2 mythic bosses (pretty doable and puggable for HC raiders) hoping you get the end boss drops off your weekly vault. 
That’s not how it’s worked in any prior tier and I don’t believe it’s changed.
If you have never killed a boss on a given difficulty it’s loot cannot appear in your vault on that difficulty, with the exception of tier pieces.
You cannot for example loot a mythic spymaster’s without having at some point in the tier killed mythic silken court, you can however loot a tier helm, and that tier helm will be the ilvl it would have dropped from silken court.
Once you have killed a boss on a given difficulty it’s loot is added to the pool for your vaults for the remainder of the tier, as is every item from the bosses prior. This is to prevent players killing specific bosses to unlock the vault that drop items they want and avoiding ever killing ones that drop things they don’t.
I am not too sure about it. If I remember correctly. The loot table is based on the “highest number” boss kill. For example you killed 6/8, your loot table will consist of 1-6th boss, you wont get loot from the final boss.
Also say if you kill just nexus princess+brood mother then your loot table will also consist of 1-6. i think Blizzard fixed this a while back to prevent people sniping for loot and just killing the bosses they actually want stuff from.
Again…this is UNCONFIRMED info based from my memory and understanding. if somebody can correct me…by all means do it.