I am just as stupified as you are. 1. No, I do not have any information on Elizabeth's marriage to a Mr. Hall. I tried to find a marriage record under the name Elizabeth Freeman and didn't find it. I don't know when she died or indeed if she did get remarried. 2. Joshua Freeman. This is just an educated guess that this Joshua Freeman is the same Joshua who married Elizabeth Denning. If not, we have two Joshua and Elizabeth Freemans in the same area. My guess is that the first Elizabeth died, and then he married Elizabeth "Betsey" Denning. You should send for the Joshua Freeman's civil war record. It would be worth it considering your big road block. Yes, because of that 1860 census in Martin Co., and given he is the only Joshua around that I can find, I am making a big jump in conclusions that this is the same Joshua that married Elizabeth "Betsey" Denning. Jerome, Indiana is where Joshua Freeman was living when he enlisted in the Civil War. I would suggest looking at Jerome, Indiana records for further clues. I don't know what county Jerome is in. It would require some Googling to find out.
3. These children's birthdates are the real stumpers! I guess records can be deceiving. Perhaps they list Elizabeth Denning, but perhaps she is the adopted mother since the conceptions are out of wedlock. Perhaps a couple of them belong to the other Elizabeth. However, it just doesn't make sense with Francis's birthdate. Some records are in error and sometimes they are transcribed incorrectly.
4. The only "pension" record I found was the application for pension online on Ancestry. You should order the complete pension record as these more than often mention a complete list of children. And if this is the same Joshua, you should be able to figure it out from the complete pension record. E-mail me before sending for the pension record because there is a private institution in D.C. that delivers much more complete records.
So many questions and loose ends; however, one cannot discount the fact that Harvey Freeman was living with Elizabeth Denning Freeman's brother and sister in law. Mere coincidence? Probably not. One would wonder, why are they not with their mother?
I hope I have addressed all of your questions. I'm just as confused as you are, but this just means we both need to look at this closer and order more records.