After restarting it did not publish any SSID. I connected through
Ethernet and I was able to go into luci with my browser (http://anygw/).
In Administration > Network > Wireless I could see the SSID modes were
on "Client"
 
put the modes to ap, then it will work as an access point.
 
Then I tried by upgrading it with the factory.bin image.

Factory.bin image is only for when you flash from tplink firmware. Once you have a libremesh or openwrt installed, from then on use the system upgrade image.
 
I had the same results, but this time I see the mode for the three SSIDs
is "Unknown".

- How do I check those things through commands?

connect an ethernet cable, type in "ip r" and try and get into the router's terminal using SSH and your IP, something like this:

ssh root@192.168.1.1

you can configure the wireless file in /etc/config/wireless

first make a backup:

 cp /etc/config/wireless /etc/config/wireless.bak

if you screw things up this makes it easy to get back.

you will need to know how to use the terminal editor vi (press i to insert text, cursors to move around, escape to exit insertion mode and :q to quit without writing and :wq to write changes. other keys do unexpected things, like d and d again removes a line of text, so make a backup before using.)

also have a look at /etc/config/network and /etc/config/lime

- How can I have this router working? I guess there must be something
wrong in the image, as everything worked ok with LiMe 16.07

much of the documentation for openwrt should also apply to libremesh, as the projects are forks (who thankfully, are going through a merge) so if you can't find enough info about libremesh, have a look at the openwrt documentation if you have more questions.

best!