I currently work for a small business. We currently have 7 employees. Because we have under a certain amount of employees is my employer exempt from paying overtime pay (i.e. time and a half)?
Also, my employers requires us to work 40 hours per week to be considered Full-Time, which affects our vacation time, pay, sick days, personal days etc. I thought "Full time" was somewhere around 32 hours per week.
What is the requirement for Part Time employees?
Are there any state regulations on vacation time? (i.e. is it required? length required, if any, probation period until it is effective)
Thank you for your help.

Because we have under a certain amount of employees is my employer exempt from paying overtime pay (i.e. time and a half)?

Not because of the number of employees. However, IF the employer grosses less than $500,000 per year AND does not engage in any interstate commerce whatsoever, he may be on that basis.

Also, my employers requires us to work 40 hours per week to be considered Full-Time, which affects our vacation time, pay, sick days, personal days etc. I thought "Full time" was somewhere around 32 hours per week.

Full time is whatever the employer says it is. It is quite common, and quite legal, for full time to be set at 40 hours.

What is the requirement for Part Time employees?

There are none. Only two states have any regulations regarding what is and is not considered part time, and Oklahoma is not one of them.

Are there any state regulations on vacation time? (i.e. is it required? length required, if any, probation period until it is effective)

None whatsoever, in any state. The closest that any state comes is that in some states, IF vacation is offered, any accrued but unused vacation has to be paid out on termination. But NO state requires an employer to offer vacation time, in any amount, to any employees.