The democrat party arose out of the splintering of the Democratic Republicans as early as 1820, with Aaron Burr and Andrew Jackson the standard bearers.
The Democratic Party was founded in 1928, two years after Jefferson died. It was founded 24 years after Burr's political career ended, and during a time he was in semi-hiding. He was not a standard bearer for anything, and was instead using a false name.
In the 1824 election, Jackson was defeated by Adams, who had the backing of Jefferson. Jackson used the press to call Jefferson a "scoundrel" and a "damned Republican."
You are going to have to provide a link for this. Jefferson made it a point to retire from politics. John Quincy Adams was supported by Clay, but not by the retired Jefferson.
Burr was one of the founders of the shameful democratic party.
See that is where I start not believing your other unfounded claims. Burr was not a founder of the Democratic Party, or even in politics at the time. He was in semi-hiding.
Marshall let Burr go, but there was never any doubt of his guilt.
The only piece of evidence against Burr turned out to be a forged letter. Without evidence, there was no way to convict him.