Is it possible to host several companies/customers in one instance of Alfresco?.
What I mean is that we need a solution where we can create several Customers (I guess that would be spaces on the first level) and underneath them a structure of projects. These Customers (spaces) should be completely separated from each other (i.e the projects/members should not be able to see each other)
Yes. Alfresco's permission model certainly supports this.
After you create a Space, you can "Invite Users" to the space and limit access to only those users (or groups of users). By deselecting the "Inherit Space Permissions" check box you will disable any and all permissions from higher level spaces.