If one is able to perform Salaat correctly but because of privacy and modesty concerns is it okay to perform it in the car sitting down; since there is no other alternative to making Salaat on time?

By "privacy and modesty" do you mean you'll have to bend over in front of men??  Personally, if I'm in a public place (say a park for example) where there are men and there's no place i can postrate, I'll pray sitting.   However, at work i just aked my boss to let me use his office.  I locked the door, prayed, and said thanks with a big smile on my out.    At my university, we had a women's lounge so I prayed in their.  Ladies would watch.  Some would ask me what I was doing afterwards.  It was great da'wa.

If one of the five Salaat's are missed should the missed Salaat be made up first or should we perform whatever the current Salaat is then go back and makeup the missed one next?

I was taught to first pray the current salat, then make up the missed one.

If one breaks Wodoo before putting on his socks and no Salaat has been performed yet, then puts his socks on (has not performed his Salaat) and then later performs Wodoo again to makeup for the missed Salaat does one need to take the socks off or is it still okay to wipe over them even though when one at first had not even performed Salaat with the initial Wodoo? I hope I didn't loose you on that one *lol*

I never make mas'h over socks.  I'm just not comfortable with it, personally.  However,  I was taught that the socks have to have been put on while in a state of purity.  Here goes some hadith:

Said al-Mughirah ibn Shu'bah, "I was with the Messenger of Allah, upon whom be peace, one night during an expedition. I poured water for him to make ablution. He washed his face and arms and wiped his head. Then I went to remove his socks and he said, 'Leave them on, as I put them on while I was in a state of purity,' and he just wiped over them." (Related by Ahmad, al-Bukhari and Muslim).

Al-Humaidi related in his Musnad that al-Mughirah reported, "We said, 'O Messenger of Allah, may we wipe over our socks?' He said, 'Yes, if you put them on while you were in a state of purity."

The stipulations by the jurists that the socks must completely cover the foot to the ankle, and that one must be able to walk (a distance) in them alone, has been shown by Ibn Taimiyyah in his al-Fatawa to be weak.

Does one always need to say Azaan before performing Salaat? If yes should it always be out loud? I was at the mosque today and I heard a man (past the salaat time) announce and he was the only one there. What about for females? Should we also say it out loud?

I never do it myself.  There's nothing wrong with it if you want to, but it's not an obligation.   Here goes a hadith for you:

Said Ibn 'Umar, "There is no azhan or iqamah for women." (Related by al-Baihaqi with a sahih chain.)

This was the opinion of Anas, al-Hassan, Ibn Sireen, an-Nakha'i, al-Thauri, Malik, Abu Thaur and the people of "juristic reasoning." Ash-Shaifi, Ishaq and Ahmad said if they make the iqamah and azhan, there is no problem. It is related from 'Aishah that she would make the azhan and iqamah and lead the women in prayer, standing in the middle of the row. (Related by al-Baihaqi.)

Hope this helps in sha allah