I think many of your questions are answered, and found with a bit of Mr Googles help.
Ones I haven't seen, and I am interested in 
are:
what is a good way to enclose the arduino in a weather proof container? (tupperware with dessicant inside?)
My starting thought is a water proof torch/flash light, maybe with some plumbers PTFE tape, and epoxy to seal holes, but I am planning on using IR for data comms so it may solve problems which you don't have.
Is the LCD essential in the device? It requires a reasonably transparent piece of enclosure, which may limit your enclosure choices.
RS components sell watertight cases, and so may be a reasonable place to start http://uk.rs-online.com/web/search/searchBrowseAction.html?method=retrieveTfg&Nr=AND(avl%3Auk%2CsearchDiscon_uk%3AN)&tfgSearch=Y&N=4294954595&Ns=I18NPrc1_uk&Nso=0#resultArrow
To make searching easier, you might want to look at the appropriate standard definitions for types of enclosure. These apply in Europe:
then google for a match, e.g. ip65.
HTH
GB-)