I have noticed "da" is used when the word after comes attached in front of the first word in English and situation is that the word after explains which kind of the first word. For example "bathroom" is actually "stanza da bagno" but it is usually shortened to "bagno"
"location of" is using "da"
"del" is a contraction of "di" and "il", but "di" is not used for this as it is used more to say "made of" rather than explain "which kind of" or even more specifically "from where". For example "vasca della porcellana" would be a porcelain tub or a tub made of porcelain.
http://italian.about.com/library/fare/blfare153a.htm prepositional articles http://italian.about.com/library/fare/blfare114a.htm simple prepositions http://italian.about.com/od/grammar/a/italian-preposition-da.htm http://italian.about.com/library/fare/blfare157a.htm di http://italian.about.com/od/grammar/a/italian-preposition-di.htm http://italian.about.com/od/grammar/a/italian-prepositions.htm
"vasca" means "tub" and there are other kinds of tubs besides a bathtub.
"bagno" means "bath"
"stanza da bagno" means "bathroom"
"vasca da bagno" means "bathtub"
That being said, "stanza da bagno" is often shortened to "bagno" and so they can't very well shorten "vasca da bagno" to "bagno". That would be confusing. So people use tub for bathtub. That does not make it redundant if we use the whole term instead of the abbreviated term, because the abbreviated term stands for the whole term in the specific context only. Without that context, it has a broader meaning.