It is possible that you can get an honorable, but if you have less than 180 days of service you might receive an entry level status separation
rather than either honorable or general. It can never be upgraded and would still deny you the GI bill, but it isn't seen as punitive like a general discharge.
As for your second question, I'm not sure what you are asking for really. There isn't a regulation that outlines what VA benefits comes with each separation. There are about 15 different statutes and regulations that, read together, indicate what each gets.
Regardless, it's not really that complicated.
Entry Level Status: Nothing but service connected injury coverage.
General: Everything but GI BIll.
Other than honorable: This depends. The VA makes an independent determination on the facts, so there isn't a clear cut answer. Sometimes it is treated like a general discharge and somethings it's treated like a bad conduct
Bad Conduct Discharge: Nothing.
Now, you aren't being court martialed, so you can't get a dishonorable or Bad conduct. You aren't being separated for misconduct, so you can't get an other than honorable.
The only options available for your command is Entry level status (if you haven't served 180 days), Honorable or General.