Translated - @gmtem, please do translation to english before posting here by yourself, then more people might help 
2 I don’t understand the question - it may be due to the translation tool" I moved K9 from the S7’s internal memory to the SD card (on the advice of the fr.fonelab.com site) "
Yes, I understood that you moved K9 to SD card - I just did not understand my translation of your 2nd question:
As I do not understand french I checked on www.fonelab.com but I did not find anything about K9.
1 What exactly is the behavior?" I no longer receive emails on K9, but I can send them to the recipients
Ok, this I did not check, as there did not come new mails during my short test period. Might try later again when I find more time…
3 Putting it back in the internal memory doesn’t help?" I did the reverse manipulation, which went well, but didn’t restore the situation (except maybe the sending, I hadn’t checked before) P/Info I have 7 accounts in imap 3.05 GB in data, 3.01 GB in cache. I don’t know what the cache is? How is it defined? And if it is possible to reduce it? What are the consequences of clearing the cache (as proposed by the K9 settings)?
Ok, this seems to be the most interesting part: 3.05 GB data / 3.01 GB cache. I guess you see it in Android’s Settings / Apps / K-9 Mail / Memory.
Cache is a intermediate storage of data used by app containing data it fetched before. To speed up app’s performance it stores data some data additionally in cache.
For me I have 118 MB data and 90 MB cache. When I clean up cache all still works fine - but is immediately filled again.
I would say it is safe to clean cache.
You say that you use IMAP for all accounts. Normally only the latest 50 or 100 mails should be kept in K9 - all the others are fetched from server when requested.
How many mails do you have locally available in K9? If it is only those 50-100 , do these mails have many large attachments? Trying to find out how to reduce your local memory footprint with K9