1. Regarding the available space on disk.
You will need an amount of free space on disk equal to the size of all of your files you want to back up.
If you have a lot of data, if you can, maybe it's better to create several backup jobs, instead of one big backup. (Like, MyMovies, MyPictures, TVMovies, TVShows, MyData, and so on). In this case, the requirement for available space would reduced to the require space for the largest backup.
2. Mirror backup.
I would want to know what kind of Mirror backup you try to use?
There is the regular Mirror backup, that indeed would replace the existing backup.
There is the Incremental Mirror backup, that would first back up all of your files, and then later, it would back up only the files that were changed. (Fast, and less space on backup disk)
3. Using the minimal amount of hard disk space.
Can I ask you where you want to back up your data?
Is it an external hard drive?
Is it an internal hard drive that is always attached to your computer?
Is it a network drive?
4. I guess it's important to know exactly what kind of errors do you have.
Can you paste here some errors from the log?