How to calculate signature generation, signature verification, transaction verification speed? I read this post on Bitcoin Scalability. 
As far as I understand sequence of steps in Bitcoin, simplified version of performing transaction should be following:

On Sender's side:


Create transaction
Generate signature and sign
Broadcast the transaction to peers


On Peer's side:


Get the transaction
Verify signature
Verify transaction
Pass to the next peer. - ???


//if a peer is a miner


Collect transactions into block
Calculate PoW for the block
If found include it to his version of the blockchain
Broadcast the block (with nonce and targe)


Other peers:


Get the block
Verify that PoW for block is Valid
Include the block into their version of the blockchain


I would like to understand Bitcoin's performance speed at every step in general or given my specifications of the laptop if possible.
How I can calculate signature generation, signature verification, transaction verification, block PoW verification, **etc speed?**
All of these things you want to calculate are highly dependent not just on the hardware you use, but the software you use. For example you can generate signatures many different ways and every bitcoin wallet generates them a little differently. The signature generation performance of Java in bitcoinJ is going to different than that of Go in btcwallet is going to be different than that of C++ in bitcoin core and so on. In addition, deterministic signatures are going to have a different performance profile than non-deterministic signatures and so on.

That said, if you really wanted to, you can run some performance testing on any one of these, though not all of them exist. For verifying signatures in btcd, there is a benchmark test that you can use.

Note that block verification (or creation) necessarily means verification of all transactions in the block as well as checking the proof-of-work. Checking the proof-of-work, by the way, is really as simple as a calculation of a double-sha256, or a single "hash" that mining gear can do billions or trillions of per second.