1. After performing a search for available rooms, I want to add a link to each room instead of just having the name, price and a 'Book' button. It would also be good to add a thumbnail so customers can see what the rooms look like. Where / how would I add this in?

=> Please edit in file rooms_booking_results.tpl.php (sites\all\themes\md_hillter\templates)

2. Also I would like to be able to remove the 'Units' text from the search result without affecting any functionality. If you could point me to where I can do this that would be fantastic.

=> Do you want to remove only text Unit or both Unit + 1 ?

You choose option "Show availability of individual units" (admin/rooms/config/bookings), so the link of Unit Description can not be got. This option only shows fields that belong to Unit Types: admin/rooms/units/unit-types.

You can go to admin/rooms/units/unit-types, add a Link field. This field stores the link of a Unit Description node
Then you enable module DEVEL, open file rooms_booking_results.tpl.php (sites\all\themes\md_hillter\templates) and add the code:

 <?php dsm($unit); ?>

For ex:

<?php dsm($unit); ?>
<?php
     print render($unit['unit']);
     print render($unit['price']);
     print render($unit['book_unit_form']);
     print render($unit['book_unit_form']);
     print render($unit['field_unit_thumbnail']);
?>

Then, the links will be shown when searching, which are highlighted in orange. You just need to print those values