Normandy

...some quick answers...

(a)...plenty of public transport...
(b)...no problems with access...
(c)...in Bayeux there are good, cheap tours from the Hotel de Gare just beyond the railway station...alternatively head for the Tourist information office...
(d)...there are hostels in Bayeux and Caen...
(e)...apart from all the usual sites associated with WW2, there is an excellent WW2 museum in Caen and the old fortress of William the Conqueror...in Bayeux the tapestry is a must-see and the cathedral is also impressive...

I found Bayeux to be an excellent base for the region...it survived the war virtually intact and is visually very appealing although a little quiet at night...the hostel is hit and miss as the owner is getting on a little and can appear eccentric to some although I wouldn't put you off staying there...Caen is bigger (400,000) and livelier at night...

Best of luck!

For your question # 1

It wont be easy without a car but the cheapest way of travelling through this area is the green coaches
http://www.busverts.fr/_hiver/plan.asp
hoping you can read french.
You can start with these coaches via either Caen or Le Havre from a ferry point of view.
Arromanches (artificial port) , Colleville (Omaha beach), and Ouistreham (Juno beach) are listed as bus stops.
Being a local and sharing also the same center of interest (war sites) i am thinking of many others that wont be accessible
by bus, only by car.
Good luck