Technically the only players mentioned signed for the next 4 years:

PCA
Nico
Bregman
Dansby

These 4 have signed contracts through the next 4 seasons.

These players the Cubs have control over with their service time noted:

Amaya 2.130
Busch 2.045

They only have signed contracts for this season. The Cubs can choose after each offseason if they want to offer them a contract or not until they reach 6 years of service time. For the first 3 years the team can offer whatever contract the team wants and the player only recourse to play baseball is to sign that contract. Universally except for very rare occasions it's a 1 year deal for around league minimum.

Once they compile 3 years of service time which they will this offseason they have the ability to arbitrate their contracts. But it's still up to the club to decide whether they want to offer a contract and almost always offering a 1 year deal.