2. If war had broken out during Reconstruction would it presumably would have brought military Reconstruction to an abrupt end and moved the reconciliation spirit of 1898 up by 25 years. But also there is no Compromise of 1876. Is the result just a longer Jim Crow Era?
I'm pretty cautious of saying that it would have that way..
Forrest and others former Confederates like Longstreet were very much out of step with other Southerners, and Ex-Confederates. Reconstruction had hardened the average Southerner against any kind of reconciliation in the 1870's and 1880's due to all the shenanigans by Radical Republicans who were still in control. For example, in 1874,
after the prospect of war with Spain, Radical Republicans hijacked an election and you had the vicious Battle of Liberty Place in New Orleans where an organized army of Ex-Confederates soundly defeated a large Louisiana State Militia force of black troops, (just about the only color of troops allowed....) under the command of Longstreet, causing a whole big mess of anarchy.
Forrest was able to make his offer because he and Tennessee had won. Thier Radical Republican government had been swept away and Tennessee was in the Union and free of Northern control, and I'm sure he and others were willing to prove their loyalty to the Union after that. Other Southern States that were still under military occupation like Tennessee had been, were fighting the Federal Government that allowed corrupt Northerners to ride rough shod over them and would have greeted a war with Spain as a new thing in their favor.
The South could have:
A. Pledge loyalty to the Union and try to help in order to free itself of military occupation and really oppression.
B. Use it as an opportunity to fight back, tying up Federal troops from reaching Florida and maybe hoping the Spanish and British would take advantage of it to offer support and "liberation" of the South from its US oppressors.
This is where we get to why Grant didn't let a war happen. The US was in court against the British suing them for compensation for all the damage caused by ships and guns they sold to the Confederacy, with some in Washington threatening invasion of Canada if the British Empire didn't pay up with interest. Add to that multiple States in an underground rebellion in the South, and that at this point in time Spain was a close ally of Britain. (Which was a different situation in 1898 as it was under Germany's influence then.)
It had too much potential to be an utter disaster for the United States fighting against the British and Spanish Empires abroad, and ex-Confederates at home, (who would probably get support from those Empires), and to top it all off the US was going through a depression brought on by the Civil War.
Grant does not get enough credit for averting that potential screw-up of all time, and it is forgotten now. There was literally no way for the US to win, yet you couldn't get that through the heads of many Radical Republicans in Congress, and the leadership of the US Military, (Sherman and Sheridan), who I wouldn't be surprised if they thought we could win.
Sorry for the long post, but a lot of ground to cover.