1. Not completely true. For Genjutsu, handseals are not always necessary. In addition, the answer that I was looking for was "The user usually releases their chakra into an opponent through the use of one of the five senses." Certain Genjutsus are conveyed through eye contact, others can be conveyed through sound or touch.
2. Depending on the Genjutsu, the target might be able to move while within the Genjutsu. Generally, Genjutsus interfere with the senses of an opponent. An opponent might see something that isn't there, or they might feel pain from a blade that isn't actually there, etc. Depending on what they see or what happens to them in the Genjutsu, an opponent might not be able to move.
Question 3:
How do you get out of a Genjutsu when one is used on you?