1)

"a la" means something similar to (in [subject]'s) "style", "fashion".

So "arroz a la cubana" would mean something like "cuban <em>style</em> rice" or "rise <em>as prepared in</em> cuba",

"una pelicula a la Tarantino" would mean "a Tarantino <em>style</em> movie" or "a movie <em>that looks like something Tarantino would do</em>."

"De" means "from", so "arroz de cuba" (and not "arroz de la cubana") would mean "rice from cuba", as in <em>'imported from cuba'</em> and not necesarily done or prepared/cooked in their style.

"Arroz de la cubana" would actually mean "<em>cuban woman'</em>s rice" or "<em>cuban [female subject]'s</em> rice" depending on context, since 'cubana' acts as a modifier for "la". Insted you could use "arroz cubano" (since arroz is a masculine word), meaning "cuban rice", but without the preparation/style add-up of "a la".

You may also found the male form, "a lo":

"a lo loco" meaning "in a crazy/sensless way/style".

"a lo Juan Gonzalez" meaning "done in Juan Gonzalez' style/way/fashion".

2)

As Aday said, it's used because it affects both the huevo AND plátano.

Cheers!

1) "Arroz a la cubana" is the name of the plate. If you say <em>de</em> you would be changing it. The preposition <em>a</em> recalls the same meaning as in English <em>à la</em><em></em>.

2) It is used <em>fritos</em><em></em> because the adjective affects both nouns <em>huevo</em> and <em>plátano</em>. So it is basically talking about a fried egg and a fried banana.

Muchas gracias Eoni y Aday! Ya lo comprendo :D