Did you receive any emails from your site before?
Do You have any email related error in AbanteCart error log

2. In case you can not access admin you can locate error log directly in the file /system/logs/error.txt

Do not post all the errors or warnings from your log. Try to point only exact error record(s) that is related to the question or problem you report.

You able to set up shipping methods to work with one Location only. In admin-extensions-Shipping edit Free Shipping method and Select India location in the Location: dropdown. To create and configure Locations go to Admin-System-Localization-Locations

Hello.

What latest thing you do on your site (upgrade, core files modify)?
What is latest errors from AbanteCart error log?
Try to clear AbanteCart cache

The question remains - can two different wt classes be selected within product pages (on different products of course)  or must one choose one wt class for the cart and only use that calculating the correct portion on each product page?

Hello. Yes, you can buy two products with two different weight classes.
All calculation based on your base weight class and other settings

Hello.

Try manual update http://docs.abantecart.com/pages/upgrade/manual.html

Hello

Check your credentials twice. And check errors in AbanteCart error log file

Hello.

You can access your contact us page with link http://yoursite.com/index.php?rt=content/contact
To add new menu item use this settings (see screenshot)

Seems there should be some corrections made here =  either the calculation/reporting needs to be better or the ability to change the Wt Class type WITHIN the prod page should be removed and set and showing only whatever is selected in the system settings. 
Lee

Hi.

Please check you weight class settings (Base weight and all coefficients (multiplicative factor) for other weight classes) http://www.abantecart.com/ecommerce-documentation/52-admin-user-manual/system/localization#Weight%20classes