Yes. When you are in the basket you won't notice any movement because the balloon itself moves with the wind.
No, because the basket is very stable you won't suffer from motion sickness. Also we don't fly above 1200m approximately, so you won't suffer from altitude sickness.
No, because the burners give off a lot of heat and the balloon travels with the prevailing wind so the wind sensation is zero. We always advise to wear the clothes that you would normally wear on the day of your flight. It's not necessary to bring additional clothing.
You shouldn't. Professional opinion and research says that because the balloon basket is suspended in the air and isn't in any way part of a ground structure then the feeling of vertigo isn't experienced.