Does a Macbook Pro 13 inches (Mid 2012) come up with a Mac OS X install disc?...
No. Macs that came standard installed with Lion or later don't come with media, and, indeed, some don't even come with DVD drives to run media in.
...What if some problems will occur regarding the OS? How can I fix it?...
Such Macs come with a hidden recovery partition. You can boot from that and restore the OS if that's what's needed, or run Disk Utility to repair the HD. Check out http://support.apple.com/kb/HT4718 for details.
My solution to your query is to make a USB thumb drive. This alleviates you from depending upon a good Internet connection or relying on Apple servers to be in operation.
I have used this procedure with success: