And Arabs tend to spell their names a certain way when transliterating them to English. If you were to spell Arwa as "Arwaa," I would think that the second A denoted a ع or something, rather than a long vowel. The choice by the course makers to denote a long vowel sound by repeating the vowel letter is actually quite odd. Arabic is rarely romanized that way. We normally use a macron for the long vowels, or don't denote the difference at all. See: https://en.wikipedia.org/wiki/Romanization_of_Arabic
it is a variant of an alif (the vowel form) called an alif maqsuurah (a shortened alif)
Tbh the rules of when to employ an alif and when to employ an alif maqsoorah are a bit complicated at this stage of learning, best to just think of it as a different way of writing alif.
To be completely accurate, there is a very subtle sound difference between an alif and a shortened alif but the difference pretty much unheard unless one is very versed with Arabic sounds.
So for practical purposes best to consider it as an alif vowel pronunciation at this stage.
hmmm, alright, since yu asked... this may be a long explanation :D
it is primarily aesthetic, its function is 'softening' the word, where a regular alif (alif mamdoodah or 'stretched alif') may mess up harmony.
as a result, it follows strict rules of placement. The rules, as I stated, are complicated. Here is an example of several:
A shortened alif is placed in nouns that have more than three letters provided the letter preceding it is not a yaa2 (ي) مستشفى مصطفى
EXCEPT when there is a difference in meaning depending on a version with a stretched alif and a version with a shortened alif يحيا v/s يحيى
and EXCEPT when the word is borrowed from elsewhere other than classical Arabic: أمريكا أوروبا except certain proper nouns that have some connection to Arabic (like a name originally Hebrew or influenced by medieval Arab culture): عيسى بخارى
and that is just nouns, there is a whole other set of rules and exceptions and rules in the exceptions for verbs, pronouns, etc.
which is why it is easier to just know which words have them at this stage...
For pronunciation, the best I can explain it - it is NOT a short vowel like a fat7a ( َ ) but: it is very close to a long vowel like a regular/stretched alif, the difference will likely not be heard unless one is very familiar with Arabic sounds. But, it subtly ends with a very soft 'h' (much softer than an English h as in hat).
Basically, the way you end a regular alif is aa (if at the end of sentence is your breath dies down with the voice still in it, so the volume lowers down until inaudible). The way you end an alif maqsoora is: as your breath dies down and just before the volume is inaudible, the voice is gone so it becomes a voiceless breath or a very soft 'h' - the h being at a lower volume than the 'a' preceding it.
In arabic terms, that would be like a vowel (halfway between long and short) BEFORE the letter (the only case where a vowel is pronounced before the letter) h, and the h is at a lower volume.
Imagine below uppercase letters at a regular volume and lowercase letters at half the volume, and a smooth transition: ARWAah
I'd argue that it's the other way around: it normally means "strange," but sometimes means "stranger" or "foreigner." Generally speaking, when it is used as a noun, it means "foreigner"; when it is used as an adjective, it means "strange." And it's not a neutral term either. It refers to being "foreign" in a way that emphasizes the fact that foreign people feel out of place, either to themselves or to the natives around them. So it would sound a bit impolite even if it referred to the fact that Arwa is a foreigner. A more neutral term for "foreign" would be أَجْنَبِيّ.