UMPI - BA in Accounting plan

[ss20ts]

There are 2 terms per semester - Term 1 and Term 2. There are no sessions. 

No. These are sessions, not terms. The word "session" is all over the YourPace website. 
Moreover, Jessica and Cody use the word "session" in their communications. The academic calendar for YourPace also exclusively uses the word "session".

The UMPI system calls them Term 1 and Term 2. As do emails from Jessica and Cody.

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I see, I don't have any accounting experience. I will aim for four terms then, hopefully 5-6 classes/term won't be too many. If I did Business Calculus from ASU and wanted it to be on the UMPI transcript, will it show up as Calculus 1, or as Business Calc? Also, if I'm done with all the subjects at UMPI and math is the only remaining class, will it be possible to do the ASU one and request a transfer in the end and graduate, or will I have to pay for another term?

No it will not be called Calc 1 on your transcripts. Keep in mind that when you apply to grad school that they usually want transcripts from everywhere you've completed courses so they go by the place where you took the course not the transfer credit.