@ Jose – the php errors you posted are completely different and not similar in any way. What is related overall and something new that I just found out about WordPress 4.5 is this: https://wordpress.org/support/topic/read-this-first-wordpress-45-master-list?replies=7#post-8274461
Previous to WordPress 4.5, error messages and other warnings that originated in the PHP and MySQL database systems were being suppressed, or hidden from the users. On the whole, this is not a great solution for long term, because while the systems usually “work” even with these types of errors, it is better to find and fix errors when they exist.
So, WordPress 4.5 removed the error suppression code from the database system. This may cause assorted warnings that you did not previously see. It is important to understand that WordPress 4.5 did not *cause* these warnings, it simply stopped hiding them from you like previous versions did. The errors were already there.
It is also important to note that these particular issues are rare. Uncommon. They only happen with very specific conditions, usually in older hosting environments. The easiest way to fix them may be to simply have your host update your hosting service to a newer server, or to migrate to a better hosting system in some manner.
When I do this Google search: mysqli_real_connect(): (HY000/1203): User already has more than ‘max_user_connections’ active connections in the Google search results are saying pretty much what the php error is saying – you have maxed out on database user connections temporarily. On my web host I get 200 active DB connections at a time. If 201 DB connections are made then I see this same error. On my web host I cannot change or increase the max_user_connections setting because I do not have access to the MySQL server files to make a change. In any case 200 active DB connections at a time is actually much higher than most other web hosts allow. So anyway if you are seeing the php error occaisonally then that just means you are temporarily maxed out on DB connections. If you are seeing that php error constantly then you need to contact your web host about this issue/problem.
Not sure why you had to manually activate BulletProof Mode. No one else has ever mentioned this type of issue/problem with any BPS Pro versions including BPS Pro 11.7.1.