1) The processor upgrade should be possible.
2) SSDs do not have spin speeds. It sounds more like you have a 500GB SATA HDD. You should be able to replace that with any other SATA SSD without issue.
3) You may or may not be able to change the graphics card.
4) You do not need to change your OS, though I would consider it.
Laptop upgrades are not for the faint of heart. It's very easy to miss something on rebuilding or damage something in the process which, effectively, bricks your system. If this is a tertiary system that you can live without, go ahead. If this is a system that gets used regularly, I wouldn't attempt it.