Keep the selected value after submit

Answer 1

As mentioned in the comment above unless you're storing the value in a database and pulling that out each time your best bet would be either a cookie or localstorage. Personally I've found localstorage to be easier to work with and unless you need IE7 support you should be fine to use that.

http://caniuse.com/#search=localstorage

You could try something like this (untested):

// On submit
var pickupdatehour = $('#pickupdatehour').val()
localStorage.setItem('storedPickup', pickupdatehour);

// On the pages that have the select box
jQuery(document).ready(function () {
  var loadedPickup = JSON.parse(localStorage.getItem('storedPickup'));
  $('#pickupdatehour').val(loadedPickup);
});

Edit: Sorry missed that it was name not ID in your select box. Use the select[name=pickupdatehour] instead of the #pickupdatehour as a selector.