1- The chances are very very low. Protected sex+no visible symptoms on her genitals makes the risk too low to worry about.
2- Unless you have symptoms (sores, discharges...) I wouldn't get tested, but maybe you would want to test to ease your mind.
3- This is a question I can't answer. The decision is up to you. I can tell that your risk was very very low but I can't assure you have nothing.
4- Yes you can. IF you had an infection you COULD pass it to her.
5- See 3. This a personal decision. I can give you a "risk assessment", then you have to make the decisions.
6- Your exposure was brief, protected, you saw no visible sypmtoms on her and when you asked her about STD's she told you she was clean (even she showed you recent tests). In my opinion the risk for skin-to-skin STD's (the only ones you could be worried about) are too low to be concerned,but I am not a test result and I cannot give you a 100% accurate answer.