There are people alive today with Neanderthal DNA and other humanoid DNA. Are they considered as fully descendants of Prophet Adam?
Scientific theories are relative, Islam is absolute. We do not mix what is relative with what is absolute. We understand what is relative in the light of the absolute. Islam says it clear: All the mankind descend fro Adam : " هو الذي خلقكم من نفس واحدة " Surat AlAraaf , Aya 189 . Also hadith "كلكم لآدم و آدم من تراب " from Khutbat AlWadaa "the final speech" .
As for the answer to your question "
Is everyone alive today a descendant of Prophet Adam (AS)?" Yes, we are. Here is a Hadith for the confirmation of my statement as well;
Abu Huraira (RA) reported: The Prophet (SAWW) said, “Verily, Allah has removed from you the pride of the time of ignorance with its boasting of ancestors. Verily, one is only a righteous believer or a miserable sinner. All of the people are the children of Adam, and Adam was created from dust. - Sunan al-Tirmidhī 3955
Our religion is based on prophecy, in particular on the prophecy God has given to Muhammad (p.b.u.h)
Science is based on observation and logic. God has given both abilities to mankind:
The ability to receive His commands was given to the prophets and the ability to direct our thoughts in dua is given to us all - not to all of us to the same extent and not without limits, but it is given to all of us who learned to pray.
The ability to observe and conclude, thus understanding the world around us was given to us all, too - not to all of us to the same extent and not without limits, but it is given to all of us who learned to think.
We can observe that God has never revealed anything that went beyond the possibilities of what the prophets were able to think.
None of science has come onto into mankind through prophecy and none that has been revealed could have been found out by mere observation.
Both abilities are limited.
If now our knowledge what we got through observation and reasoning exceeds what could be given through revelation 1400 years ago, we need not reject it.
In this sense, the scientific answer to your question is that mankind did not have only two ancestors.
The answer from revelation cannot be changed. We should think about what was the message God wanted to give to the people of the time and what is still relevant to us.
It would exceed the scope of this question to answer this and my thoughts on this topic may not be relevant either.
God knows better.