Is there individual soul. Are they infinite in number? Is the world infinite?Who is managing this universe? What is the purpose of all this happening in our life ?
Wow! You ask profound questions my friend! :) I wish I had all the answers. But I know the One who does. :)
As to your question "Are there an infinite number of souls?" The answer, in my understanding is no. The souls God created are finite in number. Some faiths speak of a hall of souls. And it has a finite number of souls God created who will be assigned to their earthly counterparts. But at some point it runs out. I always thought it was Biblical but I have learned that it is extra-biblical. Not found in the canonize Word. I first heard of the concept from a popular movie in it's time over here called "The Seventh Sign". So, though I cannot back it up with scripture, I do think that there is a finite number of souls that God created to be incarnated on this earth. And one day the last one will be assigned.
"Is the world infinite?"
I think that is kind of symbolic in nature, so particularly hard to address in the literal sense. But because I don't want to assign meaning to your question that you didn't intend, I'll answer literally. And that is "No." :) The world is simply our home for a span of time. It's limited to it's physical existence in the third plane that we inhabit. So far as I am aware.
"Who is managing the universe?"
God. That's one that's easy to answer. lol There is a measure of free will that is given to us to "rule ourselves" if we so choose, though that is not God's plan for us.
"What is the purpose of all this happening in our lives?"
God's plan is that we come to know the Son, who is Christ the Lord, through study and then responding to a spiritual invitation to come to know Him contently. Wherein we become infused with a measure of His Spirit. And then we try to give Him Kingship over our lives.
Much of what happens in our lives we experience is preparation for us to come to know the Son. And if we do have a relationship with Him, then it is often to draw us back in close to Him and get back to the center of His will for our lives when we decide to go it alone. Or be our own king. In many cases it's to let us recognize that though He made us wonderfully capable creatures, that truly we are helpless in the grand scheme of things and need His direction. To be in His will for us gives glory to the Father. It's a form of worship. And when we do this, then God rewards us. Sometimes physically but mainly spiritually.
Other times, hard times come to us to strengthen us. Strengthen our faith. Or make us stronger physically or mentally. Sadly we are not immune to the laws of nature that He too sat into place. We undoubtedly go through hardship at times because we are part of a fallen world. A world that has grown cold to Him sadly and that has grown increasingly evil. Often our suffering is due to that.
I hope I got the context of your question correct. You left me free to extrapolate what I would as it wasn't a black and white answer. lol I did answer it however to the best of my understanding and I hope it was some help to you. Feel free to follow up with me in case I garnered a different meaning from your question than you intended. :)
Thanks and God bless!