Can spirits possess dolls?

Yes, demons can attach themselves to anything material as long as it is a cursed object.

In the Old Testament people worshipped false gods, which were images made by people of stone and wood. But God had commanded this:

Therefore watch yourselves very carefully, 16 so that you do not become corrupt and make for yourselves an idol, an image of any shape, whether formed like a man or a woman, 17 or like any animal on earth or any bird that flies in the air, 18 or like any creature that moves along the ground or any fish in the waters below. 19 And when you look up to the sky and see the sun, the moon and the stars—all the heavenly array—do not be enticed into bowing down to them and worshiping things the Lord your God has apportioned to all the nations under heaven. Deuteronomy 4

Therefore, if anyone worships a doll as if she was God demons get a right to attach themselves to that doll.

When you buy old stuff from eBay you don't know the history behind that piece.

But what you have described would be an alarm bell for me. I would not purchase that doll. Demons are real.

Also, make sure you are saved so that no demon ever will be able to drag you into hell, which is also a real place.

How to accept Jesus Christ as your personal Savior and Lord?

It is the easiest thing in the world. Just close your eyes, focus on him and pray something like this:

"Lord Jesus, I repent of all my sins and I ask you to wash me clean. I am sorry for all the bad things I have done and the many times I broke God's Will. Please forgive me and fill me with the gift of the Holy Spirit. I want to belong to God. I want to be adopted into his family as his son/daughter. I want to get to know you. I want a relationship with you. Come into my heart. I give you control over my life. Please lead me through the Holy Spirit and make your Word real to me. Fill my soul with the peace that surpasses understanding and help me change so that I may lead a life that is pleasing to you. I want to go to heaven and I want to be called by the Fathers name. As of today I declare that I belong to you". Amen

If you do this with all of your heart you will start noticing subtle changes inside of you and step by step your life will change. I am speaking from experience.