Help with AES decryption with AES-NI Instructions
This answer is based on Intel® Advanced Encryption Standard (AES) New Instructions Set whitepaper (Revision 3.01, September 2012) by Shay Gueron.


No, the keys are not identical (within order) for encryption and decryption. The first and last key used in decryption are indeed the last and first one used in encryption; but the other decryption keys are the encryption keys with an additional InvMixColumns applied (usually by way of the AESIMC instruction in a preparatory step), in reverse order.
No, the sequence of operations is not as described in the question; it shall be, for AES-128:


XOR with $K_{10}$ (the last and 11th key used in encryption);
for $j$ from $9$ downto $1$:


apply VAESDEC to the result using $K^\prime_j$ (the image by InvMixColumns of the $(j+1)$th key used in encryption);

apply VAESDECLAST  to the result using $K_0$ (the first key used in encryption).





Rationale: having InvMixColumns pre-applied to (the bulk of) the round keys allows to combine them in the decryption flow after InvMixColumns, rather than before in a realisation of decryption that inverts encryption step by step. Presumably, that's easing pipelining constraints. It works because InvMixColumns is linear, that is $\operatorname{InvMixColumns}(X\oplus K_j)=\operatorname{InvMixColumns}(X)\oplus \operatorname{InvMixColumns}(K_j)$.