Well, welcome to the forum. First, I want to say that the answers to most of your questions will be here on the forum, but you're going to need to do a bunch of research. I would recommend starting now, and reading through each new post from start to finish, to start to understand what is going on. The more you read over the next couple of weeks, the easier it will be to get your degree.
I will try to answer some of your questions here, and then just start reading (an hour a day maybe) to try to get the info you need.
There is no secret to testing out, and all of the Big 3 allow it. When you have 90+ credits between all of your transcripts, go ahead and apply and send in your transcripts, and see where they place all of your courses.
Yes, it's totally possible to go from 33-120 credits in less than a year (a lot less if you're really motivated).
Not sure what you mean about "are the credits easily transferred?" If you mean are the credits easily transferred INTO TESU, then yes.
There are no requirements except that you're a HS graduate and over 21, and even then, you can get a waiver.
If you post a list of courses you've taken already, including whether it was a CC or 4-year college, and the course number with the name, that would be helpful. I can create a spreadsheet for you so you can see which courses you need to take to finish your degree.
CLEP/DSST exams are not textbook specific, meaning that they are fairly general. Most of them an be studied for in a variety of ways; online through YouTube videos, with courses you can listen to on iTunes University, with a textbook, with InstantCert flashcards, etc. If you are military, you can take them for free. Right now, DSST is letting you take exams for free, and then if you don't pass, you can retake them for free after 30 days. This is not the norm - usually the military makes you pay for the 2nd time if you didn't pass the first time.
Here are the CLEP exams:
https://clep.collegeboard.org/exam
Here are the DSST exams:
Exam Fact Sheets | DSST | Get College Credit
You can also take Saylor courses for free, and then take the exams for $25:
Earn College Credit | Saylor Academy (only look at course that are on the list of ACE or NCCRS approved courses).
You can take courses via Straighterline (a mix of quizzes and final exam) for $99/mo plus a course fee (business courses include the eTextbook):
Online Business Courses for College Credit | StraighterLine
There's also study.com, make sure you pick ACE-approved courses as well:
Online College Credit Courses - Online Classes with Videos | Study.com
There are more, but it would be too much to write here.
There are 2 pieces of good news for you at TESU; , the BSBA with a concentration in Hospital Healthcare Administration can be taken without taking the Capstone course at TESU - you can take the Strategic Management TECEP exam instead, for $114. That will save you a bundle. And, CSU-Global has 9 Healthcare Admin courses/exams available the will fit into your Area of Study (you need 6) and all 9 of them are UL courses. So you are totally set for being able to get the courses you need! They are $250 each, and you enroll as a non-degree seeking student, and each course/exam comes with the online study materials you need to take the test.
So, post your completed (or in process) coursework, and we will help you figure out the rest.