Difference between page table and inverted page table
An inverted page table is just a hash map.  An inverted page table always fits in DRAM because it is proportional in size to the DRAM. 

A DRAM total space is divided into $N$ page frames. If the size of a page frame is 4096 bytes, then the DRAM is of size 4096 $N$ bytes.
Assuming that an inverted page table entry is 16 bytes, and considering that there is an entry for each physical memory frame, then the page table is of size 16 $N$. This corresponds to 16/4096 = 1/256 $\approx$ 0.4% of the memory.

Your picture of the inverted page table is not correct.  Here is the picture from the original paper about inverted page tables (Huck, Jerry; Hays, Jim: Architectural Support for Translation Table Management in Large Address Space Machines, Int'l Symp Comp Arch (ISCA-20):39-50, 1993. doi:10.1145/165123.165128.)



It's a hash table.  Each entry of the hash table needs to store both a virtual address and a physical address.  The virtual address is there to check for hash conflicts.

The reason you can guarantee the total number of entries for the HPT (hash page table) plus the collision resolution table is just $N$ (the number of physical pages), is that there can be only one entry in the tables for each physical page.