Is the Umrah of Shawwal considered Tamattu‘ for Hajj for someone who performed it from Jeddah, then intended Hajj and entered Makkah two weeks before the Day of Arafah without Ihram? And does this entail a Tamattu‘ sacrifice, or is he considered Mufrid? And is the Umrah of Ramadan valid for the parents?

If you performed 'Umrah during the months of Hajj and are performing Hajj this year, you are a mutamatti' (one who performs 'Umrah then Hajj in the same journey) and must offer a sacrifice (hady), especially if you are not residents of the area around Al-Masjid Al-Haram. You are not required to enter ihram upon returning to Makkah; rather, you enter ihram for Hajj from Makkah on the Day of Tarwiyah (8th of Dhul-Hijjah). As for the 'Umrah performed by your parents in Ramadan, it is valid. However, if they intended to perform 'Umrah from Egypt, they owe a compensatory sacrifice (dam) for not entering ihram from the miqat.