This was fun, thanks for posting it - hopefully my answer is correct! 

>! [![enter image description here][1]][1]


  [1]: https://i.sstatic.net/NHpxh.png

Explanation:

>! **16D = 24** since this is the only 2-digit number that can be written as a factorial, and **4D = 8xxx** since 8128 is the only perfect number that is 4 digits, and since 2D is a two-digit number, the difference cannot be less than 8000.   
>!  
>! Therefore: **4A = 84**, **5D = 44**, and **1A = 22**.  
>!  
>! Now if we look at 4D again, we can see that 8128 - 2D is between 8128 - 28 = 8100, and 8128 - 20 = 8108. Note that 4D ≠ 8128 - 29 = 8099 as this would result in 8A starting with the digit 0. So **4D = 810x** which means that **8A = 14**.    
>!  
>! Therefore: **18D = 98**. Also since 17A is a multiple of 5, it must end in the digit 5 or 0. Since 19D cannot start with the digit 0, it must start with the digit 5. Since 21A starts with an 8, it must be 87 or 89, but combining this with 19A since 59 is prime but 57 is not we have **19D = 59**, and **21A = 89**.  
>!  
>! This next step is important! We have that **17A = xx95**, so 5 x 10D = xx90, a 4-digit number ending in 90. Since multiplying by 5 is the same as multiplying by 10 and dividing by 2, 10D / 2 must end in the digit 9, meaning that 10D ends in the digit 8. So we have **10D = xxx8** but since 10D is a year living people were born in, 2018 and 2008 won't work since this would result in 13A starting with the digit 0. Therefore, 10D is a year in the 1900s, or **10D = 19x8**. Using a calculator to check all of the possibilities for the third digit of 10D such that 17A = 5 x 10D + 5, we determine that **10D = 1978**, and **17A = 9895**.  
>!    
>! Now we see that 20A is either 43 or 45, meaning that **15D** is either 22 x 43 = 946, or 22 x 45 = 990. Using what we know about 17A, we can see **15D = 990** and thus **20A = 45**.  
>!    
>! Therefore: **6A = 1010**, **1D = 21**, **2D = 20**, **4D = 8108**.... I'll post more later for those interested!