Could these people be elected President?

[J. J.]

Somebody who meets all of the qualifications, except they were born in a U.S. embassy in a foreign country.
Yes

Somebody who meets all of the qualifications, except they were born in a foreign embassy in the U.S.
If his.her parents were US citizens, yes.

Somebody whose 35th birthday is the day after Election Day.

If before being sworn yes (and there is precedent in Congress)

A convicted felon who had been released from jail after serving a term without parole.

Yes

A convicted felon who had been released from jail after serving a term with parole.

Yes

A convicted felon who had their conviction overturned while in jail.

Yes

Somebody who had lived their first fourteen years of their life in the U.S., moved out, and have been back in the U.S. for less than fourteen years.

No, but they could serve one the 14  years are up.

Somebody who was born in the U.S., moved out before their fourteenth birthday, and have been back in the U.S. for less than fourteen years, but overall has lived in the U.S. for greater than 14 years.

No.

Holds dual citizenship.

Yes.

Previously renounced U.S. citizenship, but has since become a citizen again.

Probably

[J. J.]

Previously renounced U.S. citizenship, but has since become a citizen again.

No.  The US will nto allow you to gain ctizenship after you renounce it.  Once you renounce your status as a US citizen, you can never be one again.

Suppose Congress passes a law stating that you can.  Is their a constitutional bar?

[J. J.]

Previously renounced U.S. citizenship, but has since become a citizen again.

No.  The US will nto allow you to gain ctizenship after you renounce it.  Once you renounce your status as a US citizen, you can never be one again.

Suppose Congress passes a law stating that you can.  Is their a constitutional bar?

In that case you would probably count as a naturalized citizen.

Why?  You are a citizen by birth, a "natural born citizen," you are currently a citizen, and you've been here for 14 years.  I'm not seeing a constitutional bar.

[J. J.]

Previously renounced U.S. citizenship, but has since become a citizen again.

No.  The US will nto allow you to gain ctizenship after you renounce it.  Once you renounce your status as a US citizen, you can never be one again.

Suppose Congress passes a law stating that you can.  Is their a constitutional bar?

In that case you would probably count as a naturalized citizen.

Why?  You are a citizen by birth, a "natural born citizen," you are currently a citizen, and you've been here for 14 years.  I'm not seeing a constitutional bar.

You stopped being a natural born citizen the instant you renounced.   If you regain your citizenship you would count as a citizen by the means you regained it. 

The US takes renunciation very seriously.  By doing so you sever all ties with the US.

My point is, that might be in legislation, but it is not in the Constitution.  If Congress wants to pass a law (ill advised as I might think it is) that says "re-claiming" citizenship is as simple as a declaring you are citizen again, he probably could constitutionally be elected.

I can assure you, I would not support the inaction of such a law.