Some tattoo shops also pierce, but typically if they use the term "body art" in their name they will do both. I don't know if you have tattoos or have ever been in a shop, but they're not that intimidating actually! They have to be kept really clean and they typically have interesting art on the walls and will play good music. I've only ever met one tattoo artist I didn't like too, they're typically very sweet people!
You can look at the shop's website to find their artists' portfolios so you can see the types of piercings they typically do--but I bet everyone can do basic earlobe piercings! You will need to make an appointment. I generally tip for any service but the percentage varies. I'm not sure what the standard would be for piercers, but I think they'd appreciate anything!
The procedure should feel like a sharp pinch, but that shouldn't last too long! And the feeling after is just a dull soreness, tenderness to the touch and maybe some warmth. But if it's really red and hot (not warm) and swelling, then you can go back to the piercer for them to help you out. The piercer will give you all the instructions and all that you need to prevent that from happening though!
The rest of your questions should be answered by your piercer! They know the best metal and size for a new piercing. I can say though that it generally it takes 6 weeks or so to change them, I remember trying to change out my friend's piercings in middle school because she got cute earrings for her birthday, but it was too early and hurt to take the old ones out.
I hope you have fun with your new piercings!