I have completed the entire Chinese course, although I did test out of the first part of it. Now what do I do? I note that the various lesson sets all show "Level 1/5". Does this mean that there are more levels, as in 2, 3, 4, and 5? How do I access the more challenging levels?
Congratulations for finishing the entire Chinese tree!
What you do next depends on what you want to do. Levels up to 3 include new material I think and levels 4-5 tend to bring have exercises of the "translate this to english" type.
I'd recommend first to gauge your level. A good way to gauge your level is to perform "timed practices" on the Web UI (go to the Web UI shop to buy "timed practices" then you can access them from the Learn page by clicking the practice/dumbbells icon).
The "timed practice" will provide you with 1 minute. Every question you answer correctly adds 6 seconds to the timer. If the timer reaches 0, the practice stops. When the practice stops, you get 1XP for each correct answer. There are at most 20 questions. (Figures may be inexact but it's the rough idea)
Now, each timed practice will only test a few lessons at a time, so you should try to perform many timed practices if you want to cover the whole course. Considering there are 88 lessons, I'd say: try to do 45 timed practices (1h30).
If you always answer all questions perfectly, then it means Duolingo content is too easy for you and you should try harder content (books, movies, etc.). Otherwise, it's probably a good idea to get back to lessons and increase their levels.
As you noticed, each lesson has 5 levels.
The first level (L1) of each lesson has between 2 to 5 sessions.
The second level (L2) of each lesson has as many sessions as the first level.
The third level (L3) has L1 + L2 sessions.
The fourth level (L4) has L3 + L4 sessions.
The fifth and last level (L5) has L4 + L5 sessions.
(Looks like a scaled Fibonacci sequence ;-)).
So to summarize, completing all levels of a lesson will require between 24 and 60 sessions (so 12 times more than just finishing level 1).
You will access the more challenging levels after finishing each level.
You may wonder if there is a best order to do all these levels and sessions. There are 3 methods of ordering your lesson which I've read about:
Duolingo recommends the "hover" method which is described here: https://making.duolingo.com/whats-the-best-way-to-learn-with-duolingo
Some people repeatidly do lessons until they finish level 5 of a lesson before going to the next lesson.
Some people do the "hover" method with tree subparts (so get 1st part of the tree to L1; get the 2nd part of the tree up to L1 and increase 1st part to L2; get the 3rd part of the three up to L1, 2nd part up to L2, 1st part up to L3; etc.)