Current default time zone: 'America/Lima'

There is no such configuration in Joomla 1.5; there's just UTC offset (such as -5). This would indicate you're on Joomla 1.6, which we are aware there is a bug with the offset (Joomla went from Offset to Timezones, so we need to calculate the Offset from that timezone). More on this bug and patch proposal at the following forge ticket.

forge.joomlapolis.com/issues/2283

However, when a user registers in CB, it registers using the Universal time and not the Local time. I guess other functions of CB are using the same time.

Registration time, etc.. is not based off local. It is based off UTC followed by your Offset. So if it's 16:00 and you've a -05:00 offset then the time would be 11:00.

We don't have a direct cause of the session issue. It could be any of a number of things. You can try disabling the low level checking by making the following core edit.

IN: administrator/components/com_comprofiler/plugin.foundation.php
ON: Line 19
FROM:
[code type=php-brief]
define( '_CB_SPOOFCHECKS', 1 );
[/code]
TO:
[code type=php-brief]
define( '_CB_SPOOFCHECKS', 0 );
[/code]

More then likely is due to misconfiguration as is the common case or 3rd party conflict. Rarely do we find it to be a hosting environment, but it's possible.