First time I went in, first floor... can you guess yet?

Lamps!

I have to admit I laughed a little out-loud. It was 'order', though, so I could easily do them alone and proceed further. Of course it took quite a bit of time running even though it was 'only' 4 lamps.

Later on, I was defeated by the normally around level 19 bat, Barbastelle, who was hitting me for around 500 points of damage (critical hit). Granted, I was a Samurai at the time.
Basically, it seems just like the old floors, except the Notorious Monsters (and only those) seem a lot stronger.

I fail to see the point in having to progress randomly (since otherwise you will be able to only go one floor at a time, starting from 1, and obviously you wont get far in one run, or any run for that matter).

Time-Sink?

Of course it's a bit early to say much.
I do like going there either way, and always did hate the daily limit as well as the 3 character requirement but that does not affect me much.