SQL Server asks for 100GB for a dump with 1GB
Yes, it is conceivable. You probably need to shrink the source database files before making the backup. Run sp_helpfile on the source database to see the files and sizes; when you restore from a backup, it will create those files at exactly the same size, though you can move them to different drives/directories.

If the log file or any of the data files are unnecessarily large, you can shrink them, do a new backup, and the restore will use less space. Just beware of performance implications if you get in a continual shrink/grow/shrink process.