There is a set list of verbs that use "être" instead of "avoir". (It's somewhat long, but once you know it, those are all the ones you need to know.) You can find them here: http://french.about.com/od/grammar/a/etreverbs.htm
L'oiseau est tombé may be translated as either 1) the bird fell, or 2) the bird has fallen (tombé is the past participle). Both are accepted. Yes, the sentence about "les deux frères sont morts" may be either "the two brother died (or) have died" or "the two brothers are dead". The difference is that "mort" may be a past participle or an adjective.
Most verbs used "avoir" to conjugate compound tenses. "Tomber" is one of a relatively short list of verbs which use "être". They are sometimes called verbs of movement which is a bit misleading because they don't all involve movement and other movement verbs (marcher, etc) do not use être. You will have to learn which ones (there is a link above provided by rogerchristie. All pronominal verbs use être in compound tenses, too.