What is required of me for my Hajj to be valid after arriving in Jeddah from Egypt for Hajj, without having entered into a state of Ihram from the Miqat, and after having performed an 'Umrah in Dhul-Qa'dah, entering into Ihram from Al-Tan'im, thinking that by doing so I had become one of the people of Makkah?

One must enter into the state of Ihram for Umrah from the Miqat, with the precaution of entering Ihram slightly before it for air travel. It is not permissible to delay Ihram. If your intention for the journey is to perform Umrah and work, then you are obligated to enter Ihram from the Miqat. Whoever passes the Miqat without entering Ihram must offer a sacrifice (a sheep slaughtered in the Haram and distributed among its poor). As for Hajj, one enters Ihram from within Mecca.