Are the poor deprived of earning rewards and good deeds due to their financial inability, while the rich can buy good deeds with their money?

If your intention by "buying good deeds with money" is to give charity to the poor and spend money in various avenues of good, then this is permissible and desirable. Allah Almighty says: "The example of those who spend their wealth in the way of Allah is like a seed [of grain] which grows seven ears..." [Qur'an 2:261]. And if your intention is sincere, then Allah will record for you the reward of what you intended. However, if your intention is to give money to someone who performed a righteous deed in exchange for their good deeds to transfer to the buyer, then buying good deeds is not permissible due to the elements of ignorance (jahalah) and gharar (excessive uncertainty) involved.