Opening a probate estate is done by filing opening documents with the court. The exact type of documents that need to be filed depend on the value of the estate, who the petitioner is, and whether there is a will.
Yes, a lawyer is needed to open a probate estate.
No, the person who opens the estate (signs the petition to probate) is not automatically appointed as the administrator. The court will appoint the person who is most appropriate depending on (1) what the will, if any says and (2) what family or other interested persons might be willing and able to serve. If you have an interest in the estate, you can request to be appointed as the personal representative, but that does not mean you will automatically be appointed.
If there is some question about whether potential heirs are really entitled to a share of the estate, you can contest their eligibility. They would then need to demonstrate to the court's satisfaction that they are eligible as heirs (or children), which might include DNA testing.