@Fredrick Hock Your contractor is giving you just that, an estimate. The reason he might not be able to give you an actual fixed number is because in construction there seems to always be something unexpected once you start opening up walls. He could give you a quote for doing specific work, but there is always the chance that something else needs to be done that isn't part of his scope that he would just create a change order for.
You can't protect yourself from going over budget due to unforeseen circumstances, you just have to add a percentage for contingencies.
As far as keeping a contractors team on schedule, make sure you thoroughly vet your contractor. What jobs is the GC currently working on? How many in-house workers does the GC have? What work does the GC subcontract out? If your contractor subcontracts out most of the work, then he can have an issue staying on schedule because he is at the mercy of his subcontractors especially if he is hiring the cheapest labor to stay within budget. If he has an in-house team that is large enough, he can easily add more workers to speed up the project as long as he isn't spread too thin because he is working on multiple jobs.
If you hire a good contracting team that you can trust, you won't have to worry about micromanaging them. Don't hire on price alone, their price is usually the lowest for a reason.