It doesn't look okay to me. The leaflets seem to have curled which can happen with too little water. But that doesn't necessarily mean it's had too little water in the pot, it could also be damaged root system. Damage roots could also be if where you bought it they had recently repotted it. Do you know if it got very cold at some stage? It can be difficult isolating the problem as there could be a number of reasons. Using a wooden skewer to push down into the potting medium can show if there is enough moisture deeper down. If the skewer comes out clean it'll be too dry. If it's wet down there you'll see that when you pull out the skewer. Other than that, as palmsandsnow said, you just might have to wait a few weeks to see.

Thank you so much for the reply, really appreciate it.

Palmandsnow, indeed there are some new leaves and they are not dying but just looks so skinny and weak but maybe thats normal. I will Google the picture of dying and healty palm and for sure i will wait and hopefully it will be ok. Thanks a lot

Troppicbreezent, i did what u said with the skewer stick and it was clean, thats why yesterday morning i decided to spray water to the leaves and surface of the soil a little bit too. Just now i hang humidifier at every heater in my house. So i hope it will help too. And yet wait for few weeks more. Thank you so much

one more question, should i cut the dying leaves or i must wait till it completely die.

Have a good day

While a leaf still has some green, it still holds food for the plant. If you want to cut the leaves off, then yes, wait for the leaves to die completely/turn all the way brown. But then again, many date palms (especially tall ones) actually look quite attractive with a sheaf of dead leaves hanging at the side of the trunk, but it is your choice!

By skinny and weak, do you mean the whole crown, each leaf, or just the tree as a whole?

Also, do the dying leaves feel dry and crispy, or just kind of floppy?

Good luck!!

Hi palmandsnow,

at this moment some of new leaves are still stand and some looks weak. The dying leaves are dry and crispy.

Thank you

Could you post an update picture? I feel like that would help a lot.

If the leaves start drying further up in the crown until their are only a few green ones, then something is definitely wrong with your palm. But, if after a couple of weeks/months, it looks roughly the same, then you only have a small problem, if any problem at all.

Have a good day!