"Instead" means "in place of." Sometimes "instead" is used in place of the word "rather." For example, from your question:
(4) I didn't lie to you. Rather, the things you heard are facts.
What subjects you use is not important so long as the thought hangs together and makes sense. For example, the following does not hang together and makes no sense:
The mail hasn't gone yet. Instead, the dogs are playing in the backyard.
There is no connection between the mail being delivered and the dogs playing in the backyard.
This makes sense:
It's too early to pick up the mail. Instead, we'll walk the dogs.
This is a choice between two activities "we" can do: pick up the mail--it's too early, or walk the dogs instead.
Some More Uses of Instead
The word "instead" can also be used at the end of a sentence, or in the middle. Let's say you're ordering at a restaurant. You think a certain item on the menu looks good.
The waitress says, "We're out of that today. Would you like this instead?"
You say, "Yes, that looks good but could I have olives with it instead of onion rings?"