adding (the) do imply some emphatic sense (like if you've heard of some new engineer but you didn't know who it was, then you know it's Lama so you ask about her). In Arabic, that would be: هل لمى هي المهندسة الجديدة؟ - as you can see, the word هي (hiya) meaning "she" was added (and in fact I can still remove it and the sentence would be correct but it's a typical emphatic style in Arabic). Anyway, the important point here, as you can see, the word that comes after, المهندسة (the engineer) had been identified with (AL) which matches the English (the). However, this is not the case above; The word مهندسة is mentioned here without (AL) so it is not a definite noun, and in English you would use (a/an) for indefinite nouns: an engineer.
Actually مى sounds like ما (long "A" sound). In the other hand مَ is a short vowel (ma).
The dotless Ya-like letter ـى is called Alif Macoorah (shortened Alif). Using it has orthographic reasons but essentially it is just like long "A" (as the regular Alif). Some names in Arabic are written with this letter instead of the regular Alif (maybe remnants of old writing style), for example موسى (Moses) and عيسى (Jesus), as well as لمى (Lamá) above.
Anyway, on other occasions, this letter has a story in writing verbs but no need to list it here - it can be too advanced.