You just gave three very valid reasons why they would require you use their equipment all,with one interlinked reason: control. That’s not unusual.
What can be required by contract is basically anything that is not unlawful. If you wish to negotiate the contract, you are welcome to attempt to do so. If you cannot come to terms that you are willing to live with, then you don’t work for them.
Bottom line: you agreed to the terms.
if it is determined you have been misclassified, the powers that be can go back in time and require you be paid properly as an employee (overtime if applicable) as well as the employee being required to pay the taxes associated with having an employee.
Yes, In one way or another it could result in losing the job.