What would be the effects if a Native American killed Andrew Jackson after the Trail of Tears?
Presumably, a Cherokee. In general Indians of one tribe didn't care much what happened to other tribes - except when they were at war with another tribe.
Also,
which Cherokee? The Eastern Cherokee in North Carolina were not deported, and in fact are still there. Of the main Cherokee group - the "Ridge Faction" were the ones who signed the Treaty of New Echota. They argued that Cherokee removal was inevitable, and the treaty provided title to land in the west, assistance in moving, and other benefits.
Chief John Ross and the majority of the Cherokee national council denounced the Ridge Faction as traitors. For several years after the removal, the Cherokee lands in Oklahoma were convulsed by a brutal blood feud between the two groups.
I don't see any Cherokee going off to kill Jackson when there were despicable enemies much closer to home.
Besides which, Jackson was not the progenitor of the Cherokee Removal. It was the state of Georgia which confiscated Cherokee land, and suppressed Cherokee tribal government, and threatened violence.
Jackson's part was to refuse to intervene against Georgia, even when the Supreme Court ruled that Georgia's anti-Cherokee laws were unconstitutional. ("John Marshall has made his decision. Now let him enforce it.")
A Cherokee enraged against whites would be more likely to kill the Georgia ex-governor George M. Troup, the chief agitator for Indian removal.
And what if this was after he was President?
That is, after he left office? Well, that's already implied, becuse the removals were in 1838-1839, under President Martin Van Buren.
How would this change policy towards Indians
It could be viewed in different ways. There would certainly be an anti-Indian reaction. OTOH, there was a lot of hostility to Jackson. And such an act would be in constrast to the attacks on settler families that Indians were typically denounced for. Some whites had recognized the injustice of Georgia's anti-Cherokee actions (the Supreme Court, obviously), and the Senators who voted against the treaty (it passed by only one vote).
I think a fair number of people would be willing to say that Jackson had invited his doom.
As with Nat Turner's Rebellion, the action would be abhorred - but it would win recognition of the motive, and a form of sympathy. ("Do you
expect them to like it?") There would be some advocacy of better terms for removals.
However, by that time, Indian removals from east of the Mississippi were pretty much over.
and how would Jackson be remembered today?
Much as OTL. There would be more focus on Jackson's Indian policies.