1. I have configured the menu option for logging in to my site.
As I understand, the menu option uses the Login module?
I am trying to hide the login module title when not logged in, but I want it visible in the module after logged in.
H9ow can i do that?
Use 2 different login modules. One accessible to Guests only and another accessible to Registered only. See below on how to use Guest access within Joomla.
docs.joomla.org/How_do_you_hide_something_from_logged_in_users%3F
2. I use menu option Forgot username oe password when not logged in. Can I enable Joomla standard ReCaptcha on this form? How?
You need to use CB AntiSpam for captcha on forgot login. We do not support Joomla captcha.