I am a native Hindi speaker. When we are taught वाक्य अशुद्धि शोधन (correct the incorrect sentences) we are taught about these little things such as why एक is required for the sentence to be grammatically correct rather than leaving it out. You all can go try those out online they are readily available it will make your hindi more refined once you learn basic sentences. :)
I didnt want fo write this cz it might confuse you even more. But because you asked.....
अं is not always nasal. It also has a 'ng' sound in slaying and if you know Korean it's the ㅇ sound in 방 and therefore the name of the letter अं is 'ung' (u as in umbrella). It sometimes has a nasal sound. They both have but as the time passed the natives screwed it up!
When a kid is taught these letters, he is told that अँ is the nasal one and अं is the 'ng' one. But as he grows up he kinda automatically learns (ofc with help from parents and teachers) certain spellings like में, हैं, करें, बदलें etc. have ं even though they're nasals. It's similar to how you know that cylinder amd cypher start with a 'c' even though they have an 's' sound.
I'd suggest you to learn the spellings. It's not much work as not a lot of words have this thing.
Good luck learning Hindi!!
Indians would usually write ladki (the ड़ is mostly represented by d), but many even write larki (or larkee for that matter, we use the Latin script just to get the point across and because it's easier than using a Hindi keyboard which we are not accustomed to owing to the fact that they came out only recently).
र - It's a soft tone of "r" Just download google translator and translate words like Night - raat in hindi (soft r)(रात)
Secret -raaj in hindi (soft r ) ( राज)
You will understand .
But when you are using "ड़" , first of all keep in mind no word starts with this alphabet and it sounds like actual prounciation of english "R" . Like when you say "Rat"," Rattle snake" ,"roar" ...how you pronounce the "r" , It's a high vocal tone. So this is how you pronounce "ड़"
You can search on search on google translator words like - To fight - लडना ( lārna) To quarrel - jhagarna (झगडना).
I hope , i have made you understand.