I believe I have seen several times that you do not recommend a third-party plugin, but I would like to know if you recommend a solution to sync the site between a local installation and an online installation
We always use the Duplicator plugin to move website between two servers (even from local to live)
It never made mistake for us :)
We need to have a pro version or the free is suffisant?
It depends on your needs, but we use the free version of Duplicator, and as my colleague mentioned, we never had problems with it.