If the company you work for states that "a full time employee may not take the day before or the day after a holiday and expect to get paid" is this legal? And does this apply only to hourly employees or both hourly and salary employees? I realize this may change state to state and this question would apply to Texas. In addition this company regards a "full time employee status" applys if you work 32 hours a week. The company will not pay overtime, as they expect you to "use a longer lunch hour to work off those overtime hours" before the end of the week.
I have been unable to clearly understand the law with regard to these two things Is this just a rule that companies are allowed to make up or is there some federal guideline they are supposed to follow.

This boils down to company policy and dept of labor standards. Yes, since the company is paying you for the day off, in which you provided no work for, then they can require you to be there the day before and the day after to qualify for the paid holiday. Understand that this is a way to ensure a consistent labor resource to fulfill a production requirement. This keeps all eligible employees from turning a 3 day weekend into a 5 day vacation that is unscheduled and very hard to recover from. The overtime issue is sticky. Typically, over 40 hours is paid overtime. 32 hours is a threshold to indicate full time employment who can be eligible for benefits. Since the US Dept of Labor has issued new standards for overtime and the associated positions, I would consult a Dept of Labor officer for that question.