We are dealing with 2 different problems.
To create a bootable USB you will need a Mavericks Installer package from Apple Store the 5.5 Gig file saved to MBA- but not run.
I used this proces to make a bootable USB:
Bootable USB
Format it, using Disk Utility, as a Mac OS Extended (Journaled) drive, named Mavericks.
This can be done from the Erase tab within the app; make sure the USB drive does not have multiple partitions (that can happen, so turn to the Partition tab to verify and correct this).
Open Terminal.
sudo /Applications/Install\ OS\ X\ Mavericks.app/Contents/Resources/createinstallmedia --volume /Volumes/Mavericks --applicationpath /Applications/Install\ OS\ X\ Mavericks.app --no interaction.
Erasing Disk: 0%... 10%... 20%... 30%...100%...
Copying installer files to disk…(this part can take 30 minutes)
Copy complete.
Making disk bootable...
Copying boot files...
Copy complete.
Done.
If problems reoccurs get another USB stick with minimum of 8 Gig capacity (not partitioned).
Repairing your Hard drive:
If the MBP boots in the Recovery mode using cmd-r then follow that process to restore your OS installation, or use the Disk Utility to check/repair the disk.
You can open the terminal and use the fsck -fy to check repair the disk.
If the problem is minor you can start in Safe mode that will correct some minor issues.