Can I get an advance on accepting the employment offer?

I would be happy to help review your offer, but, no, there are no legal requirements in employment or contract law that an employer or you must keep the terms of an offer confidential, or that the contract include any requirement that you keep anything at the company confidential. So, in theory at least, if I offered you a job at $100K/year, I could publish a full-page newspaper ad with all the terms of the contract I offered to you spelled out in the ad. (Now, you may be able to argue an invasion of privacy, but, as to the example I gave you, standing alone, I don't think you would win).

Congratulations on receiving multiple job offers. In addition to what you listed as considerations, above, you can review things such as whether these are all for employment (rather than independent contractor); whether you would be considered "at will" or would be given a number of rights as an employee; and whether the employer would provide training/mentorship etc. If I were in your shoes, I'd compare reviews of each employer, as an employer - this can be hard to find, but Glassdoor.com has a limited number of reviews of certain employers. If at all possible, reach out to some current employees at each company and ask the same or similar questions, such as "what do you like or dislike most" about your job and the employer?

Offer letters generally have similar language in that they offer you a specific job at a specific price point. However, these letters are not always standardized and you should read the letter carefully to understand what is being offered.

Employment offers can contain information about promotions, but they typically do not. Jobs and employers and situations change over time and employers don't want to get stuck agreeing to a promotion before working with you.

Potential employers are not explicitly required to disclose that a background check is a necessary condition of employment. In certain circumstances, employers must conduct background checks and keep records of these checks. This is exemplified in the Texas Administrative Code, where an employer must maintain written documentation of a pre-employment check for at least two years regardless of the subsequent employment status of the applicant. You may want to check your offer letter for terms that indicate your employment is contingent upon meeting satisfactory requirements in lieu of specific language of "background check". Depending on the industry and or the company, they may be required to do a background check to verify licensing or education in order to mitigate their risks of negligent hiring.