When if the creatures enters the area = he saves
But if he in the same round ends his turn in it, does he have to save again?

Read the last line again :) 

unfortunately, the spell doesn't target creatures

Use this spell to lube up your halfling rouge before squeezing them through a tight space to unlock a door and tell me grease aint one of the best spells in the game.

Also fun to cast at the top of a staircase, and laugh as the orcs behind you slip, fall back into each other, and all go falling down the stairs taking some sweet sweet fall damage.

Gonna have my players face a giant cow named "Your Mom" and I can't wait to use this spell and flavor it as milk

Is this a Sorcerer spell now, per Tasha's? or is that a typo in Tasha's on DNDBeyond? (I don't have a hard copy to compare)

Best spell in the game if you need lube. Although it does disappear after 1 minute and its implied to be like, pork fat or butter

what if someone stays in it for several rounds does he have to make a saving throw each round? For example. He is in a Corner and there is no space to move out of it.

1st round he got the save, standing still.

2nd round fall down. Stand up.

3rd round save again...

Or just one time, at the first contact in the area?

Possible I asked my Dm about using that and fire bolt as a cantrip on the grease and he gave me the yes I can. But it all depends on Dm

Would be great if someone could tag Sorcerer for Tasha's Cauldron update to Sorcerer spells.

we have always ruled if you set that up then light that shit up 

my apologrease

ANOTHER dnd banana peel!

Another DnD banana peel

If I was the cast grease and then someone else or me next turn cast spike growth in the same area and then push someone into it? Would they slide through the area because of the grease?  if so it would turn the floor into a meat grinder because they take 2D4 piercing damage for every 5 foot they travel through spike growth

There's nothing in the spell description to suggest that the grease is as volatile as, say, kerosene or another refined petroleum oil. Setting fire to the slippery stuff of the Grease spell would probably be like trying to set fire to a room-temperature stick of butter or wax candle by tossing it into the fire in an outdoor fire pit. Not going to happen. Don't toss room-temperature kerosene, gasoline, etc. into an open fire, though, because the results will be far more dramatic and dangerous.

Assuming that slippery stuff would burn like kerosene is as much a leap as assuming it would be edible and useful in cooking. Here's a pretty detailed discussion that makes no mention of combining Grease with fire: https://www.dndbeyond.com/posts/513-spell-spotlight-grease

If the DM rules otherwise, good for you... until it's used against you, that is. :) If your character uses this sort of grease-fire exploit, the NPCs should do the same.