But I don't understand why you have remaining data you don't want.
If you wanted to use the disk without keeping data the way to go is to remove all partitions and then make new ones + format the partitions.
But if you just modified the existing partitions and no format the data is kept - and is supposed to be kept, anything else would be disastrous as there are many cases when you want to keep your data.
To your other questions
hda used to be IDE and sda scsi, but then came SATA and sda was SATA as well. From Feisty Ubuntu decided to make all drives s and not h (grub the obvious exception) but hda still works I think, but is not recommended.
/media is the normal mount point for "non special" partitions (Like home and root)
The odd looking
is how root appears in some cases - I have not had the time to look up why. I have this in my secondary computer which has nine distros installed - this one only has five (other) distros installed and the installer has not used that option....
The lost and found folders are locked with a purpose
If there is something in them it's remains of a check by fsck were corrupted files were found
And as you mounted a home when you installed the installer made the best of the situation and put your old home folder in /home/home/guest and as you already noticed the files are from your Mandrake home and has nothing to do with Mint. As a general rule you can't do anything in your home folder that messes up Linux. The obvious exception are that you can loose personal settings for some programs stored in home.
And you must have set sdb7 as an ordinary partition else it would have been used as swap.
Now that you know you can decide if you want to make a fresh install (Keeping your home partition I suspect
) or keep "the mess"
Sorry for the slightly messy language, must have been tired - takes too long to fix