If I rename the the folder /templates/ot_sportshop/html/mod_login will it still keep the styling as it is now?
If it does not keep the styling, you can edit /templates/ot_sportshop/html/mod_login/default.php and find the code:
<input ... name="passwd" .../>
and correct the name="password"
So not need remove or rename it.
If I edit the product details page, /templates/ot_sportshop/html/com_virtuemart/productdetails/default.php and other files in /templates/ot_sportshop/html/com_virtuemart/productdetails/ how will Virtuemart know to put the information I want there?
Should I use custom fields instead?
You can export or var_dump the product variable and know what you can show. I see almost you need to show as screenshot is set-able in backend product edit.
You also can use custom fields for custom attributes.