The actual question contains LA as 38 Bits, not 438 Bit (Reference-book)
Ans for question 1:
To avoid the overhead of bringing a large-size Page Table into the Main Memory, Multilevel paging is implemented.
In multi-level paging, paging is applied on Page Table & instead of bringing the entire Page Table into Memory, the only page of Page Table bought into Memory. Or A multilevel page table reduces the number of actual pages of the page table that need to be in memory because of its hierarchic structure.
Ans for question 2:
LA=38 bits
Since the pages are 16 KB, Offsets are 14 bits (i.e 2^14 = 16 KB).
Remaining bits = 38 -14 = 24
Now this 24 bits for the page fields(i.e for outer PT and Inner PT).
as entry is 4 Bytes , one page can hold 2^12 page table entries and therefore requires 12 bits to index one page.
therefore division =(12,12,14)