Employer cannot expedite. File at the earliest possible time (see USCIS for 90/120 day limit) and pray. Remember to put a sticker with your name in your mailbox, or usps may return card to USCIS. If delayed, contact congressman, senator, file SR, go to ombudsman.
I don’t think there is an expedite option for OPT. It takes what ever time it takes
I've done this before. Short of your manager sitting on the form and not sending it back, it's a matter of the government.
I don't think your employer can do directly anything about it. As OPT is something that you apply directly with USCIS. You can request employer to help build your case through documentation. Here are few criterias for expediting your case with USCIS :https://www.uscis.gov/forms/expedite-criteria