If it mean a teacher who teaches English language, it is angoltanár (one word) and if it means a teacher who is English, it is angol tanár (two words). Just like magyartanár is a teacher who teaches Hungarian and magyar tanár who is Hungarian. So a magyar tanár can be an angoltanár and an angol tanár can be a magyartanár :D (ok, the two last sentences are so confusing, don't care about them.) - legalábbis én így tudtam... de javítsatok ki, ha rossz a helyesírásom és tévedek -
I think it's important to note this difference, as you will meet this phenomenon multiple times during your language learning journey. In Hungarian, we usually write everything separately until we don't have a specific reason to write something together – this reason usually being a change in the meaning. It might seem to be just a tiny difference in this case, but writing together or separately can totally change the meaning of the word or phrase. The rule of thumb is that you write something separately for the literal meaning and write together if there is something figurative about it.
drága kő – expensive stone
drágakő – gem
talpra esett – fell on feet (e.g. a cat)
talpraesett – adroit, nothing comes amiss to him
meleg ágy – warm bed (bed with a nice temperature)
melegágy – hotbed (for flowers)
jól esik – it's raining heavily
jólesik – it feels great, it's pleasing
két gyerekes házaspár – two childish couples
kétgyerekes házaspár – couple with two children
egyet ért – understands one (problem of many)
egyetért – agrees
Lehetne még itt sok példa, de aki ezekkel egyetért, az a példák közül nem csak egyet ért. – There could be a lot more examples, but those who agree with these, understand more than one of them.
Also, there is a difference in pronunciation too as we tend to stress the beginning of every word denoting the word boundaries. So in the phrase „angol tanár” (teacher from England) both words are stressed, whereas in „angoltanár” (someone teaching English lessons) only the very beginning. Here the audio says it the second way but it is written in the first way – which is an error in my opinion. But again, it is a very slight difference, something maybe only natives can perceive, and from the context it is more often than not obvious what you are talking about.
Still, it can lead to some funny situations or misunderstandings, so here's a Hungarian joke taking advantage of this ambiguity:
A rendőr áll kint a szakadó esőben, és eszi a szendvicset, amit a felesége csomagolt. A kollegák döbbenten nézik:
– Józsi, miért nem jössz be ide a szobába enni?
– Azt mondta a feleségem, akkor egyek, amikor jólesik.
We don't have a continuous tense but do have some other forms to express continuity or longer activity. Eg. "keresget" means repeated or longer searching for something and this or a similar suffix can be applied to all verbs. We also work around continuity often with specifying time, eg.
"sokáig", "hosszasan" = for a long time
"állandóan", "folyton" = constantly, all the time
"régóta" = since a long time ago, started way back
I believe that your suggestion is also possible, but that it would carry a different emphasis than the DL sentence.
The Dl sentence answers the question, in a neutral way, "What are you doing?" Answer: "I'm looking for an X."
Your sentence, in contrast, answers the question, "What is it you are looking for?" Answer: "It is an X that I am looking for."
In other words, by putting the direct object before the verb, as you have done, you put it more into focus.
Experts please correct me if I am wrong about this!