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Velocity is how much a team completes per sprint, averaged over several. Burndown is remaining work against time within a single sprint.
One is for planning the next sprint; the other is for noticing, on Wednesday, that this one is not going to land.
The shape matters more than the endpoint. A flat line that drops on the last day means work was being finished in a rush, or that nothing was marked done until it was all done.
A line that rises means scope was added mid-sprint. That is worth a conversation about who added it and why, not about the team.
At least three. One sprint is noise.
Scope was added mid-sprint. That is a conversation about the addition, not the team.
Only as a capacity input. As a performance measure it corrupts within a month.
Half an hour with your own data usually saves reading three of these. The guides will still be here afterwards.