How is Kate Marsh alive in "Episode 4" of Life is Strange?

First of all I have been playing the Episodes in sequence starting from Episode 1.

In Episode 2,

I clearly saw Kate jumped off the roof and died.

When I started Episode 4 today, I found that Kate is still alive and also

David Madsen was kicked out of the house in Episode 3 but he is still there in his garage in Episode 4 and thanked me for taking his side when I actually didn't.

Are these things still supposed to happen in Episode 4 regardless of the choices you made in previous Episodes?

What happened as is stated in the comments above is that you started a new game in a different save slot, the game started at episode 4 because you chose to do episode 4.

The choices you make are for 1 save slot (or game).

For example:

• Save Slot A: episode 1 through 3 (your choices, kate died)
• Save Slot B: started at episode 4 (the game makes the choices for you, kate lived)

If you play this game, use the same save slot for every episode