I have this sentence :
Today's lecture will spark a lot of discussion, and I just want to let you know that I welcome it, so please feel free to jump in.
I have three questions:
The implied subject is you (whoever is being addressed), as is commonly the case in commands, requests, invitations, etc.
[You] feel free to jump in.
[You] step this way, sir.
[You] go away!
Jump in (or common alternatives such as pitch in, dive in, leap in, etc.) simply means become completely [metaphorically] immersed in the discussion, and participate, actively contribute, say something.
The phrase is using the imperative mood, which is the mood used for requests or commands (among other cases).
The imperative mood is a particular mood, since it is used only for you; that is the reason why the subject is not explicit: It is always you.
To form the imperative mood, take the sentence in the indicative mood (simple present), and remove the subject; from "You eat onions on Saturdays." you get "Eat onions on Saturdays."
"Felt free to jump in" is wrong; the correct one is "feel free to jump in."
"Jump in" has two meanings:
In your case, the meaning is the second one.
