hi,
i really miss a feature which allows you to just explore and map the island without being chased by the monster!
i would really appreciate some kind of exploration mode! how about you?

Well... The monster is more of a constant menace for you, something to be afraid of. However, there's really, really nothing to fear - most of the time, you just have to duck in tall grass and slip away when it's not looking. And during 20+ hours that I have spent with the game, I have met the monster about 3 or 4 times - all of those encounters lasted about 5-10 minutes. The monster is dumb and rather easy to bypass, and it can't swim, so... Eh, basically, there already is an exploration mode, which is the main game. Don't worry about the monster, the worst that cane happen to you is that you'll respawn at the latest save point.

a little into the game there is an injection which permanently improves awareness. after you got that, you always know where the kitty's coming from and just have to flee in the other direction until the heartbeat stops. really no game-breaker.
if you ever play the game through you will see that removing the kitty is like removing the story alltogether, so hang in there!

(spoilers) , I really miss the tension that Milo brings to the game, after you're cured its just not as fun to explore, since hes no longer lurking about.

Apart from the Beast, darkness is another big enemy. It's very easy to get lost and fall off a cliff when darkness falls. I played this game on "easy mode" by sleeping until morning every day, but for extra challenge you could try crossing the island at night.