is soldering mobile processors something that i could do at home?
It is not possible to solder components with contacts on the bottom (called Ball Grid Array, or BGA) using a soldering iron.  You would need either a reflow oven, or a BGA rework station.

Some people do have reflow ovens at home, or have converted toaster ovens to do the job, but even then it's a bit tricky and easy to mess up.

So the answer to your question is yes, you can do this at home if you have the right tools, but if you only have a soldering iron then you can't.