No, it's stated to be 120.000 lightyears in diameter.
But that's for the Star Wars people.
For us, the star wars galaxy is almost 121.000 lightyears across, since a galactic year in star wars is 368 days (Coruscant year), rather than our 365 days in a year.
The star field you are refering to could be other distant galaxies.
And as for the hyperdrive, they may have been able to get it to work temporary in order to get to Bespin.
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