You're using three different words here, and they all mean something slightly different.
To deserve something requires an active virtue or lack thereof. For instance, to deserve punishment you must have done wrong. To deserve praise you must have done something praiseworthy. American Citizens who were born in another sovereign nation deserve to vote by virtue of their successful completion of the US naturalization process.
To be entitled to something means you are given something by another based on inborn or inherent qualities. Persons born in the United States are entitled to vote in her elections once they reach the age of majority. This entitlement is granted without prejudice as long as the initial criteria is met. However, convicted felons have this entitlement rescinded for the period of their incarceration.
So then we come to rights. Rights are inborn and are not granted by an external source. Rights can be defined, such as in the American Bill of Rights, but these definitions are not what grants you the right to something, they only affirm that the American government has pledged not to take them away. For instance, I have the right to walk out my front door, hopscotch for a block or two, fart loudly, and hopscotch back to my house. I'm quite certain that right has never been explicitly defined by anyone; I have it because I am physically and mentally capable of doing so, and it has not been taken away by any entity capable of doing so.
Since rights are inborn, not deserved, a better subject for this thread might be "What rights should human beings be allowed?"
Moving on to your rights.
1. We are entitled to equal treatment as long as we do not infringe on another’s rights.
Too broad. Are you entitled to a birthday present from me since I give one to my sister every year?
a. We deserve to be responsible for the lives of others whose rights are in jeopardy.
By what virtue do we deserve this responsibility? How is this responsibility defined?
2. We are entitled to live safely and to be our own person with our own possessions.
We should have this right (not entitlement, it is not something granted to us)
a. We deserve to be responsible over such unless our ability to do so is deemed unfit.
Not deserved, but right otherwise.
3. We are entitled to be exposed to whatever we wish and express our opinions freely.
a. We deserve to be able to withhold information for the safety of others.
Er, these two are contradictory, if we have the right to be exposed to whatever we wish then no one has the right to withhold information for the safety of others.
I would agree that we have the right to expose ourselves to whatever is legal and available. We do not have the right
not to be exposed to things we find objectionable.
