Permalink structure for blog posts and pages are managed in Wordpress Settings -> Permalinks page, so to make blog posts have permalinks like blog/%postname%/ and you've done it right.
The tricky part is about Custom Post type permalinks declaration:
in your CPT arguments declaration there's a rewrite rule parameters, which in turn has with_front - if ...
Found my problem, was actually not even a plugin conflict but an optimisation operation that had broke the plugins!
I added a couple days ago a script in functions.php that would "defer" all the scripts, which made important scripts being loaded after they were being executed.
Thanks for the help.