I had set WP_DEBUG to true.
I don’t see those warnings on my test site.
If you like, I can produce a screen-cast for you to see.
No warnings, No slow down in speed…
I don’t understand why your web hosting company cannot assist you in “removing” the restriction on open_basedir which is a server setting.
Your web hosting company does not own their servers? Maybe they are resellers of hosting account?…
By the way, that is a warning, not error.
If it’s an error, your website will not load.