Magic Jar tends to be one of those spells that's not clear on how all its effects interact with game mechanics. From what it does clarify though we know
Once you possess a creature’s body, you control it. Your game statistics are replaced by the statistics of the creature, though you retain your alignment and your Intelligence, Wisdom, and Charisma scores. You retain the benefit of your own class features. If the target has any class levels, you can’t use any of its class features
Now by RAW since Draconic Resilience is a class feature you would still benefit from its effects even though it states
As magic flows through your body, it causes physical Traits of your Dragon ancestors to emerge. At 1st level, your hit point maximum increases by 1 and increases by 1 again whenever you gain a level in this class.
Some DMs will probably not allow you to gain this effect since it is supposed to be tied to your body
Bladesong is another class feature and again by RAW you will have access to it and its effects when you use magic jar provided that you still follow its restrictions "that you aren’t wearing medium or heavy armor or using a shield."
The rules are not clear on what counts as attunement with respect to body/soul combo, there is an accepted answer here that states that when you use magic jar you dont gain the attuments of the body you posses but makes no mentions of the state of your previous attuments.
With respect to haste and invisibility based on how the spells are expected to work, I would say neither of the effects would be expected to be carried over. (There are no hard and fast rules that say this, is just what I would do as a DM)
Moving on to the charmed and frightened conditions I would leave it up to your DM as again there are no rules for this. Personally I would say you would still be frightened by your enemy (and could not use magic jar to get closer to them) and that the enemy would be charmed by the body you were in when you charmed them and not your new body unless you could convince them otherwise