Can a lawyer represent me in court to request my last name be changed without me physically being present?

I have done this in Jackson County. Other counties may require a formal hearing with the petitioner actually present though.

Someone else was driving my vehicle, got hit by an underinsured motorist now suing my insurance company.

If that person was driving your insured vehicle with your permission then under Missouri law your liability policy also covers him (or her).

Can I take my ex to court?

The answer is absolutely. For your child's future you should hire an attorney to file a Petition for Order of Paternity. The court will issues a...

Well, the practical course is to contact your employer's human resource department. They will have likely dealt with this issue before.