Yes, you can install an SSD drive in your laptop. You can use the current drive as a second drive in that computer (it supports two drives). I have a Pavilion dv7-2185 and did what you are considering doing. I had to order a bracket to get it to fit. Make sure you get the correct bracket if you do have to order one. I cloned the drive using software that came with the SSD drive. When you purchase the SSD drive you can get a kit. Internal cabling should not be an issue.
Could you tell me the ssd brand you got that came with the software that helped you move the files?