This is a good question and usually the misunderstanding of people who are curious of the doctrine.
I am going to address the second question first. When asking this question you are making a mistake in terms of what total depravity is. You are assuming that the individuals who are not called don't have a choice to repent. This is not what is believed. The person who typically believes in total depravity believes that by birth the individual is sinful (Psalm 51:5) and hates God and therefore will not look for God (Romans 3:10-11). Total depravity is not a choice that is given or not given, it is the state of a mans heart at birth. That his heart hates God because he loves sin (Romans 1:21). Nobody says that they do not have the option to repent. Rather that the individual DOES have the option to repent but they lack the desire to repent. Therefore because they don't want to repent they wont repent.
What happens to the individual that does repent is that God gives some a heart as a new gift (Ezekial 36:26). He makes the individual a new creature (2 Corinthians 5:17). God gives them a new desire for him. A longing to be with him. So because they have a desire for God they repent and turn to him. God never restricts anyone's repentance. Simply put they don't want to repent, because they don't want God. The people who do repent want God. God is not under any obligation to change a mans heart. Although He can and does. Typically they appeal to the many instances when God changes a man in scriptures or sets them apart from birth.
In the example of pharaoh, they do believe pharaoh has the option to repent. In fact it is clear that God tells him to. So he has the option to, and God demonstrates to him that he should over and over. But pharaoh hates God and doesn't want to repent and God is under no obligation to change his heart to make him want to repent. Even if God calls him to repent, because pharaoh has the option to repent. God gave him that option, and calls him to repent but pharaoh simply does not want God, and does not want to repent.
Hope this helps!