IMac – After installing SSD in 2009 iMac I only see a black screen

This site works best when using one question at the time, so the answers can be found by others for specific topic, but lets make a exception.

Your problem might be somewhere else (so we need your Console report for that) but to answer your questions:

1- Is there any way to make sure that my SSD has been replaced?

Short of opening the computer and looking at the label on the disk, from outside only way to tell is if you saved the previous UUID and compare it to this SSD in About this Mac.

2- I would like to know what does it actually do from Apple logo to login window?

It starts by finding the boot sector, then it activates the EFI (the boot loader) for OS files, after that it loads the user profile settings and apps.

There is a very good description here.

Wow, it looks like you did almost everything already. What I have left for you are reinstalling your OS X and Reset PRAM.