Cost of structural Engineer? (Just a Ballpark)
If you are planning to pull a permit, and you need the structural engineer to prepare stamped plans for you that will be used to pull the permit, figure between $500 and $1000. If you do not plan to pull a permit (this is probably illegal, I am NOT SUGGESTING IT, however I suspect many people on this forum operate without a permit), and you can live with a verbal report (unstamped obviously) from the structural engineer, figure $400 or so for an opinion on what size beam you need, and a few ideas on how to connect the beam to the existing framing.
If you do hire the SE for full price, make sure the report includes a section on temporary support during installation, and includes details of the connections between the ends of the beam and the columns, as well as details of the column connections to the footers or main house beam.