1. I have the Player's Handbook and Xanathar's Guide to everything 

2. I created a campaign and invited players and DM into this campaign

3. Can the players use the content for another campaign that someone else DM's (I am a player in the campaign)? 

4. Our Barbarian can only see  - Path of Berserker but they can read the player's handbook?

They really need a pinned FAQ or guide for this.

• An account needs a master subscription to enable content sharing for a campaign they are a member in.
• All members of a content sharing campaign will share all their purchased content with all other members of the campaign. It does not matter who has the subscription or whether they are the DM or player, all content is shared with everyone.
• In order to use shared content to build a character, that character must be part of the content sharing campaign.
• Sometimes the content sharing gets buggy (granting content to some members but not others or only sharing partial content). When that happens turn content sharing off and back on.

Hope that helps. It sounds like your barbarian is having the PHB shared to them, but their character is not in a campaign that is sharing the PHB.

Hey,

Thanks for the reply.

I have master subscription, and I have tried disabling and turning it on. I have also tried creating a whole new campaign. 

Can content sharing work like:

1. I create CAMPAIGN A and invite friends and share my content

2. Friends join CAMPAIGN B, a campaign another DM made, and use my shared content 

No. In order for characters to use shared content, that character must be in a content sharing campaign. But you can enable sharing in up to 3 campaigns, and (to reiterate) you do not have to be DM to share content.