Have reviewed your install and am noticing the first attempt to login ALWAYS fails. You have to attempt to login twice and the second time will succeed. This indicates a huge problem. After enabling debug mode and maximum error reporting there is sure enough Fatal errors present. This is likely the cause of your issue. Please review the below findings.
ERROR:
500 - JDatabaseMySQL::query: 1064 - You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'ORDER BY `id`' at line 1 SQL=SELECT * FROM `jos_content` WHERE `id`= ORDER BY `id`
SOURCE:
modules/mod_blank15v50/mod_blank15v50.php:19
modules/mod_blank15v50/tmpl/default.php:179
Disabling
Leave a comment HERE - ... (mod_blank15v50) and
Blank Module 15v50 - Visitor Counter (mod_blank15v50) resolves the fatal error, but does NOT resolve the double login or profile issue.
To remove the double login issue the system plugin
System - Expires Headers (expiresheaders ) has been disabled. This has fixed the need to having to attempt to login twice for a successful login (or having to refresh directly after first login attempt). This still however does NOT resolve the profile issue.
You mention not having caching; this is false. You do have caching, but not through Joomla or preferred method your host. You have a 3rd party plugin called
System - JCH_Optimize (JCH_Optimize) installed which is caching the output. This is the cause of the profile issue. I have disabled this plugin and confirmed profile issue is now resolved.
I recommend UNINSTALLing the following extensions.
mod_blank15v50
expiresheaders
JCH_Optimize
Please folks be mindful of what you install. Not everyone developers of the same caliber as we do; we take great pride in stability and security.