I am studying towards degrees in Finance and Managerial Economics.

Are they holding this property for some reason and not accepting offers?

I asked her to call to see if they'll accept a lower offer and she hasn't even gotten back to me.

It has no windows and no secondary emergency exit and is uninsurable in it's present condition.If there were a fire now and they were killed,the previous owner could be sued and maybe jailed for negligent homicide.Demanding and accepting one penny from them would make you criminally liable as well.You need to get them out asap and not accept any money from them.Don't give them anymore grief and be helpful finding them somewhere else to go.

We decided to put an offer on the first house, and by 10pm we had an accepted deal.

A lot of people base it on what a middle American nuclear family may want, so you may pay for the good schools and other amenities unless you can snag a deal.I am not looking for a "good" neighborhood as much as an acceptable neighborhood that fits my own criteria.

Should we accept the $245k or should we counter offer $255k?

It has been tentatively accepted but there is a relo company involved.  

Im still in school finishing my degree while I do that im just goin to keep learning new information about real estate.

First of all, what the seller will accept is not (or should not be) contingent on your exit strategy.