On their DD-214, look at Block 26. It will say "Separation Code", and a three letter code will be typed in there. See the related link at the bottom for what those separation codes mean.
Not it is not, with an other than honorable discharge you have been you can be dicharged (kicked out) for many reasons. These reasons being you conduct, not meeting weight standrads, testing positive...
In some cases, yes, in some, no. The Army tends to be a bit fickle about this (although I can't speak for other branches). The Army is less willing to reenlist a service member who received an OTH...
Almost always, you can not change your discharge from the US military from "other than honorable" to "honorable". On very rare occasions, you MIGHT be able to do this, however, you would have to...