While the rules for this can vary by state and depending upon the terms of your lease, generally the new company must honor the lease until it ends. Once the lease is up, however, they can make changes.
The new management company cannot change the terms of your current lease, but they will have the option of making changes once your current lease expires. Check your current lease for possible 'loop holes' to this standard just in case.
No, in most cases the new management company cannot change the terms. When they bought the property (or signed the contract), they took on all the existing contracts that were in force. They knew what they were getting into when they signed up.