Do they use engineers 1st draftsmen 2nd and surveyors 3rd before the construction crew build any road or bridge?

No, there is no particular sequence, these activities have to happen concurrently. You need mapping from the surveyors before you start design, then during the design process draftsmen and engineers work together to put together the plans for whatever is being built. Then during construction, the surveyors are needed for layout work in the field, and the engineers may be consulted as the project progresses to troubleshoot things.

On the design side, survey comes first, drafting comes last and engineering occurs throughout.

On the construction side, surveying still comes first, but there's very little drafting and not much engineering.

The design engineer will be consulted if there is a question about the design during construction, but most of the steps in construction occur under the direction of superintendents or foreman who usually are not engineers.

Yes, engineers are the managers of the projest then surveyers are in charge of the measurements of the site then Draftsmen are in charge of the drawings and specs to fit the site. They all work together to get the project to fit the design onto the site.

That is the general sequence but it also depends on the type of road and where and why it is being built.

In some cases there are other people involved like the environmental groups as well as lawyers in dealing with right of way and other issues.

As to who is in charge, that depends on the contractural agreements between the various parties and the owner of the road or bridge. If the contract is a cost plus contract then the owner is really in charge. If it is a fully turnkey contract then the turnkey contractor is in charge. There are all kinds of combinations as to who is in charge of what.

They use all three, yes, but together, not in sequence.

Engineering firm is in charge, and they have engineers, draftsmen and surveyors working for them.