Is it appropriate to follow up with the manager you interviewed with in order to check on the status of the position/where you stand? If so, when? how? any tips on wording/context? and how to ask for pay rate they are offering???? tysm!!!!!

The only follow up with the manager should be a thank you email or note thanking them for the interview.
Instead, reach out to the HR person that contacted you for the interview. All correspondence about timelines, status and the hiring process should go though them.
You are going to need to be patient. These things almost always move excruciatingly slow.
You can use Google or chat GPT to finesse some of the wording in your email, but make sure that you include things like how much you enjoyed the meeting the team (be genuine) and then repeat parts of your resume/experience that make you the perfect fit for the job. Really you are selling them on how you are the perfect fit for the job. They always offer low, but I gotta say, I have not had much luck in bumping up that initial offer. Very frustrating. Good Luck!