For the PERM process it is the EMPLOYER who has to conduct the recruitment (and define the job title & job duties); NOT the foreign national beneficiary. The answer to both your questions is a "yes", but employer better use the services of a qualified immigration attorney to guide it through the extremely complex PERM process.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
Yes the title makes a difference. No you cannot use a title for a position you do not occupy. Your salary can have an increase. You should be working with an experienced business immigration attorney.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.