No, you should not be able to put your finger in the "hole" of your penis.
You should ask your parents if you were circumcised tho. If you were not, then you are just putting your finger inside the skin opening on the outside of you penis, you're not putting it inside the hole. Also this red thing that opens up when you squeeze it is your penis head and your real penis hole that is opening when you squeeze it.
Uncircumcised penises often have white build up and other things around them that need to be cleaned.
Don't listen to the guy above. It looks like you are uncircumcised. You are putting your finger inside your foreskin. This is normal. We are all born this way, but some people perform an operation (circumcision) to remove the skin off the head. You should be able to pull the skin all the way back to uncover the head. This may hurt and you may bleed your first time. I am uncircumcised and so are many guys. I don't recomment getting a circumcision, it would remove sensibility and you would enjoy sex less.
You shold not be able to put your finger in your penis, and you should not have green like bumps. I would go talk to your doctor. Sorry to hear and see that you are having this problem.