Guust

You have to set the map language at GD > design > map > Default map language.

2. The meta title does refer to the CPT instead of the category. I know that is also how it works in the demo at http://wpgeo.directory/hotels/4-stars/
You can change that by using https://wordpress.org/plugins/wordpress-seo/

3. Custom fields can only be used with listings, not locations.
Your visitors can navigate to a location first, and then use the custom search to narrow it down to the listings using the custom fields of the CPTs.

1. Change location to Alwar using the switcher in your menu, then click on “View all” for each CPT listed.
http://tourelp.com/location/india/rajasthan/alwar/
>>
http://tourelp.com/places-to-see/alwar/
http://tourelp.com/deals/alwar/

2. I added the “popular category” widget to your GD home and GD listing top sections, so now you have direct links to all categories and subcategories, for example http://tourelp.com/places-to-see/alwar/history-culture/

3. If you add custom fields and you want to let people search them, you have to add the custom field to the advanced search. Like you have done with “Days fro travel”

4. Just add tags to your listings, and then you can click on the tag link from the listing detail page.

I notified the developers.

I now modified the CCS and added it to GD > design > scripts.
The other places would work too.

If you ticked “Use BuddyPress registration form” you can delete that redirect in your functions.php.
What do you mean with “logged into buddypress”?
You can only login to WP, and you do that by way of using a GD form or Buddypress form etc. Buddypress extends the WP login.

Appearance > theme options > design options > Left Background

I added this to your CSS:
#geodir-wrapper {margin: auto; width: 1020px;}

Changed your map widget to 100%