Hola Ihaasmanley: Yes. "buscan" can mean: "the look for", "the are looking for", "they do look for", "they seek", "they are seeking", "they do seek", "they search for", "they are searching for", "they do search for", and maybe some other possibilities. Please see Babella's post also on this page; there is another way to say "they are looking for" - that is to use the Present Progressive tense, which is "Ellos estás buscando" which basically means the same as "Ellos buscan" with a slightly different nuance - to much to explain here.
No clue why Duo marked "They seek stability " wrong because it should be correct, and Duo accepted that answer from me. Perhaps you made a typographical or spelling error that you didn't catch? It probably marked "are looking for" wrong because the sentence is present tense. "Ellos buscan" is "they look for," "Ellos están buscando" would be "they are looking for."
Stability is of unknown quantity and so does not get the article. http://www.businessspanish.com/LECCION/articles.htm#notdefinite Yet, the article would be used at the beginning of the sentence. http://spanish.about.com/od/adjectives/a/intro_def_art.htm
Most of the times it depends on the verb and the function the noun has in the sentence (subject, object, attribute, etc.). For instance, ser requires its subject to have a determiner, but not its attribute.
- La estabilidad es buena para la economía del país = Stability is good for the country's economy (La estabilidad is the subject).
- Eso era estabilidad = That was stability (Estabilidad is the attribute).
Evitar requires the subject to have a determiner, the object should also have it unless it's plural.
- Él trabaja duro para evitar la guerra = He works hard to prevent war (La guerra is the object)
- Las vacunas evitan enfermedades = Vaccines prevent diseases (Las vacunas is the subject, and enfermedades is the object, it does not have an article because it's plural).
Faltar does not take direct objects, and it does not require its subject to have a determiner.
- A la planta le falta agua = The plant needs water (Agua is the subject of that sentence).
Just to give you some examples, it's better if you memorise the verbs that need determiners rather than the nouns.
I have the same question! Does a general noun take a definite article if it's an object and not a subject?
The following discussion proves that rule is inconsistent, but i don't know if it's to allow for obscure contexts, or what the best translation is.
If the general noun is uncountable or of unknown quantity and is after the verb, then it won't have the definite article. http://www.businessspanish.com/LECCION/articles.htm#notdefinite