The -un ending you're hearing on "baab" is an indefinite ending, kind of equivalent to "a/an" in English, so "a (regular) door" instead of "the (regular) door". The thing is, it's usually written if it's going to be said, otherwise it's left off entirely in writing or speech (it's mostly just used in formal spoken and written contexts). So it's a bit odd that it's spoken here but not written.
This sound doesn't exist in English. We use 3 to represent ع while texting Arabic using the Latin script (English alphabet) because the two letters look visually similar when mirrored. To make the sound, try making a very low pitch. Sing a note, then keep lowering your pitch until you feel your adam's apple (that protrusion thing you feel going up and down on the front of your neck when changing pitch) is uncomfortably low, to the point where you can't sing much, yet still emit some kind of 'noise'. That's the ع
It's going to feel physically uncomfortable for you to make this sound at first, and it will remain uncomfortable until you practice making that sound every day for a month or so. It may even feel like someone is strangling you. It's completely normal for it to feel this way and to take that long, because your throat has never had to be in that position so often in your life so far, so I suggest that you practice making that sound in isolation before attempting to pronounce it within the context of a word to avoid forming bad habits.
Having said that, I highly recommend you find a native speaker that can listen to you trying to make that sound to make sure you got it right before you commit it to memory with practice. Bad habits are hard to break, so it's advisable to get it right first before practicing it to form a good habit from the beginning. Have fun! :-)
Phonetically, it's a voiced pharyngeal fricative. Just like "z" is the voiced version of "s", and "d" is the voiced version of "t", "3" is the voiced version of "h" (or pretty close). When you pronounce "h" in English, like in "hat", your vocal cords aren't vibrating. If you were to instead say "3at", you would make the same motions with your mouth and tongue, but you would vibrate your vocal cords.
If you're not familiar with voiced/voiceless consonants, try sticking your fingers in your ears and switching between saying "sssss" and "zzzzz". The "z"s should sound louder in your head. To pronounce "3", try doing the same thing with "h".
I’m not talking about voiced vs. voiceless. I’m saying that ع isn’t the letter to compare with H. Comparing it with H doesn’t help. The letters that can use H as a comparison are ح and ه Then we can talk about voiced and voiceless.
I just want to make sure that you are producing the right sound, because from your description, I’m not so sure. I hope you are in contact with a native speaker that can hear you and correct you. I’m a native speaker, but unfortunately, Duolingo doesn’t give us a way to communicate privately or send voice messages, so I can’t check it for you.
Comparing ع to h helped a lot for me - I do better knowing where my mouth and tongue should be positioned than just trying to figure it out by ear, when learning a new sound. I have spoken to native Arabic speakers (one works in my research lab!) and been told I'm pronouncing ع correctly.
I make the comparison to h because your mouth and tongue are in the same position, and you're making the same noise, just vibrating your vocal cords as well.
The voiced vs. voiceless discussion doesn't matter for ح and ه, because they're both voiceless anyway, like English h.
(Replying to the parent node again)
I appreciate your apology because it shows the kind of person you are, but it wasn't necessary. I knew you had good intentions. Aside from trying to help you, I was also trying to explain things in a way that someone who is not familiar with linguistics would understand. It's great that you have this palette of intricate positions and movements in the mouth that help you produce different sounds from descriptions, but most people don't have that and didn't spend many years studying sound that way. From a non-linguist's perspective, I found the comparison to H to be (possibly) confusing, and I wanted to make sure non-linguists reading your comments won't be confused by it that way, especially that a lot of them might not have native speakers to check them. In any case, I appreciate your input and I'm sure other linguists will, too. Have fun learning Arabic :-)
(Duolingo isn't letting me reply to your last comment below, I guess because they are limiting the number of levels, so I'm replying to this one)
If comparing ع to h worked for you, then great! You've checked it with a native speaker so it's all good. I was just worried about you forming a bad habit. From my experience teaching foreigners Arabic, their main problem is mostly with the throat rather than the position of the mouth or tongue when it comes to ع
Search on YouTube for the pronunciation and the places of your mouth that you needa use to say the words. It's really important in Arabic. And hard for us foreigners cuz we don't ever use our mouth n throat muscles to make that sounds but u will adapt after a while. The have 4 Z sounds, 3 S and 2 T.