Most of the major email providers use some kind of scoring mechanism to figure out how likely it is that an email is spam. If the email exceeds a certain threshold, it's filtered to the spam folder. The threshold changes for every receiving server, and some are configurable by the recipients.

Even your IP address/domain is important - some spam filters will flag an email if anyone with the same IP/domain has sent spam in the past.

Hi.

For whom it may concern  - this extensions integrate third party chat service to your site and some of them are free, paid or have both limited free and premium paid services. 

Hello.

What is your cart version? How many categories you have?
Do you have category names with some special chars in the name?

Hello.
You need to turn ON SSL in your AbanteCart settings
http://docs.abantecart.com/pages/settings/details.html

Hello.
You can disable Email Activation for New Customers in your admin http://docs.abantecart.com/pages/settings/checkout.html

I am also facing the problem I kept the setting on Off Mode. Still I need to Approve the New customers.

Hello. Try to clear AbanteCart cache and try again. What is your cart version?

Hello.

The menu font color is white, so when your browser window width is not enough your menu items jump to next line where background is white so it looks hidden for you... you need to remove few items from menu to make is shorter or change CSS rules

Hello.

Maybe you have enabled Seo URL's but forgot to configure your .htaccess file?
http://docs.abantecart.com/pages/tips/enable_seo.html