Thousands of same couple of warnings on my sites with K2 (and greek k2 language installed)
only when Global Configuration -> Session settings is set to PHP
When session handler is set to database warnings stops
Greater traffic more warnings
I need session handler to php because speedsup sites and the load on the database server is much much smaller especially when there are thousands of visitors at the same time
My sites without k2 have no warnings. No warnings and in one site with k2 but without extra k2 language (But with very little traffic)

mod_fcgid: stderr: PHP Warning: mysqli::stat(): Couldn't fetch mysqli in …/libraries/joomla/database/driver/mysqli.php on line 219
mod_fcgid: stderr: PHP Warning: mysqli_close(): Couldn't fetch mysqli in …/libraries/joomla/database/driver/mysqli.php on line 226

Tested on 4 different servers (shared host and dedicated)
Joomla 3.7.1 (The same problem in earlier versions)
K2 2.7.1 + k2 greek ext
PHP 7.0.19
Module and page cache on
Different updated templates from Rocket themes (Gantry 5 & 4)
checked with other plugins disabled
Let's note that if you look at google you will see thousands of sites with the same warning problem

Hello,

This is an issue from Joomla!, most likely related to your caching settings.