1. Yes you can replace the internal M.2 SSD with the 2.5′ SATA SSD, you will need a SATA data cable and some screws, you can pickup a kit here.
Because you are not replacing it with another mSATA SSD which is what is in your computer currently you will have the ability to clone your operating system over to the new 2.5′ SATA SSD (MZ-77Q2T0B)
3. If it is recoverable at home you will not need to buy anything, otherwise your best bet is to ship the drive to a data recovery company. You can attempt using Test Disk to restore your damaged partition layout and hopefully recover you data if the disk is still spinning. Click here for a guide on restoring partition layout, click here for a guide on recovering files from NTFS filesystem.
You can see here in this YouTube video, a user is using both a 2.5 HDD/SSD and the mSATA SSD