650 GB Seagate hard drive model: ST9640320AS
How your hard drive is setup.
sda= SCSI drive "a" and the numbers which follow are partitions.
sda is used now for most all hard drives, previously hda, hdb, hdc, and so forth were more common.
It no longer denotes a SCSI type system exlusively.
sda1 = a 210 MB size partition identified as SYSTEM and formatted in NTFS file system. This would
probably be the EFI partition for Windows 7 system. Oddly enough, it seems your windows 7 system
was installed as a MBR type disc and not a GPT system. That's good if you decide later to install
Linux on it.
sda2 = This is your main windows partition, the second one on the hard drive, what in windows would be seen as "C:/" drive. It's where all your system files, personal files, programs and so forth are at. It is 625 GB in size.
sda3 = This is your Recovery partition. It's the one with the data necessary to restore your computer back to factory specifications, and the one from which you would create Restore Discs. It is about 15 GB in size.
sda4 = This is a 110 MB size partition with the HP special Tools included with your laptop. Oddly its in a FAT32 formatted partition instead of NTFS formatted partition. Probably so it can be copied off to a flashdrive easily.
sda1 size: 0.21G label: SYSTEM uuid: F6CCB6EACCB6A471 fs: NTFS
sda2 size: 625.02G label: N/A uuid: 5014106B14105676 fs: NTFS
sda3 size: 14.79G label: RECOVERY uuid: E8DE7AAFDE7A7622 fs: NTFS
sda4 size: 0.11G label: HP_TOOLS uuid: 3C09-44A7 fs: FAT (32 bit)
The DVDRW drive
sr0 size: 1.33G label: Linux Mint 16 MATE 64-bit uuid: N/A
This is all very good. It means once you copy off what files you want to save, you probably can restore your computer to it's original setup, just like when it was new. Remember, to do so will lose all files you created and saved, and any programs you installed since then.
Considering your particular computer acumen or level, I'd urge you after saving what files you want, to run the restore system function to return it to like new condition. You can do that by pressing ESC key and then choosing the correct function key. Check that pdf file I linked to you on how to do that. You might wish to save that pdf file onto your Acer computer to have for consulting with at times.
After restoring your windows to computer, then run the program to "create restore discs" that should be on the computer, and be sure to have the required number of disc available first. It can run 4-5 DVD or up to 20 CD disc to do. I believe my daughter's system required 16-17 CDR disc for hers.
I would put off to the future installation of the Linux system until you've had more time to study on it. While I think it's easier than Windows and safer once you spend a couple months getting used to it, you have had enough frustration already for now. I'd look on it as a future project and one you can approach in steps. You will have the DVD which you can boot to from time to time to play around in it some, but there's an easier method to learn it first that is a lot safer. When you are ready, you can come back here and I or someone will help you install Virtual Box, then install Linux Mint into it, and there it can be safely tried out in it's own "sandbox" without risking any problem to your windows installation.
You should commit the info from those commands you ran into a text file somewhere and have them available to display again if need help in future on that computer.