Should all play happen in scenes in Fate?

Question

After reading the core rules and playing a first — very pleasant — session (I was the GM) I wonder how many time in a game should be spend in a formally declared scene?

In our last session, we played a continuous game, where I noted down "scenes" when the kind of action changed (e.g from talking to following suspects down the road) or the location changed.

As far as I understand the rules, I'm expected to inform the players of start/end of a scene and the scene aspects, so they can adapt to it, am I right?

Do you jump from scene to scene, every time formally starting it?

So, now you are on the train station, to await the arrival of John. The station is full of people.

And after this is settled:

Now that John is with you, you walk back to the harbor tavern. The tavern is very crowded and loud, but you get a table in the back and sit down.

Or do you just describe things and play "classical" and starting a formal scene if you see fit?

Answer 1

All play does happen in scenes, intentional or not.

According to Fate Core

A scene is a unit of game time…during which the players try to achieve a goal or otherwise accomplish something significant…[o]nce the action shifts to a new goal, moves to a new place related to that goal, or jumps in time, you’re in the next scene.

—Defining Scenes

Even going off of what you call "classic" play, there are still scenes, it's just that Fate is more aware of scenes since many mechanics trigger off of them. Once per scene stunts, GM fate points refresh, player stress is eliminated, etc.

As for needing to define situation aspects, it's not exactly necessary to codify them right away. As long as you describe the scene in enough detail, players will start to pull aspects out of your description. Remember, "[i]f you’re not looking for a free invocation, and you just think it’d make sense if there were a particular situation aspect in play, you don’t need to roll the dice or anything to make new aspects—just suggest them, and if the group thinks they’re interesting, write them down," (Creating and Discovering Aspects in Play).

Meaning that players will look for things they can invoke, either with the expenditure of a fate point or through the create an advantage action to gain a free invoke or two.