I sent my laptop to get something fixed (broken hinges), then I had to send it again because it didn't begin. Now that I have it back, I have realized that it is working much slower than before. My brother checked it and states that I have a different CPU. But, can they do that without asking? Aren't they suppose to replace it with one of the same type (velocity, etc.) as the one I had before?

Answer:
If you had it sent to the manufacterer? to fix the hinges they should not have touched your Processor. But you can verify this by going to their website and looking under your models' “Tech Specs” and reading what processor you're suppose to have. Then right click on your 'My Computer' icon and select properties and make sure that the processor you’ve is the factory one. (you'll see it)
Answer:
Yes.

Go to www.belarc.com and run the advisor. Print it out.

Try to find your original buy documentation and compare the processor clock speed on it to the Belarc report. If you indeed have a slower CPU then you need to contact your repair shop where the laptop was repaired and bring this to their attention.

If your laptop is a Dell you can go to their support site and enter the service tag number off the bottom. Then you can choose to get a report of the hardware configuration of the laptop when it left the Dell factory.

Answer:
if they replaced the cpu it should have been the exact same as the one they took out