สวัสดีครับ/ค่ะ ฉันสามารถตรวจสอบได้อย่างไรว่าบิดาของฉันมีพินัยกรรมหรือไม่

Under Romanian law, the fastest way to check whether your father left a notarial will is through a Romanian notary public, because notarial wills are recorded in a national register.
Romanian notaries can verify the Registrul Național Notarial de Evidență a Liberalităților, which records authentic (notarial) wills and related acts.
If you can’t travel to Romanian, you can sign a power of attorney (procură) so someone in Romania (a trusted person or a Romanian lawyer) can go to a notary and request the checks / start the succession procedure on your behalf.