Should I use https for all my web pages, even those for which secure transmisson is not needed?

Using SSL (https) causes slower page loads and uses more server resources (encrypting/decrypting the pages).

You should DEFINITELY force SSL for contribution and event registration pages IF you are using one of the payment processors for which end-users are entering credit card information on your site (PayPal Pro, Moneris, Authorize.net).

Unless you are running your entire CiviCRM site under https (which some people do because they want all contact info to be encrypted across the network), you should not use https:// in your Resource URL setting — using a relative URL is preferable as it will "switch" how the css file is sourced for sites that run some pages in http and some in https.