1.What is reason?

Reason is a cause, action or justification for an event or action 
The power of the mind to think, understand, and form judgements logically
as stated by the Oxford Dictionaries 

2. Write definitions of deductive and inductive reasoning.

 deductive argument is an argument that is intended by the arguer to be (deductively) valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument's premises (assumptions) are true. This point can be expressed also by saying that, in a deductive argument, the premises are intended to provide such strong support for the conclusion that, if the premises are true, then it would be impossible for the conclusion to be false. An argument in which the premises do succeed in guaranteeing the conclusion is called a (deductively) valid argument. If a valid argument has true premises, then the argument is said to be sound.

Here is a valid deductive argument: It's sunny in Singapore. If it's sunny in Singapore, he won't be carrying an umbrella. So, he won't be carrying an umbrella.

Here is a mildly strong inductive argument: Every time I've walked by that dog, he hasn't tried to bite me. So, the next time I walk by that dog he won't try to bite me.

An inductive argument is an argument that is intended by the arguer merely to establish or increase the probability of its conclusion. In an inductive argument, the premises are intended only to be so strong that, if they were true, then it would be unlikely that the conclusion is false. There is no standard term for a successful inductive argument. But its success or strength is a matter of degree, unlike with deductive arguments. A deductive argument is valid or else invalid.

The difference between the two kinds of arguments does not lie solely in the words used; it comes from the relationship the author or expositor of the argument takes there to be between the premises and the conclusion. If the author of the argument believes that the truth of the premisesdefinitely establishes the truth of the conclusion (due to definition, logical entailment, logical structure, or mathematical necessity), then the argument is deductive. If the author of the argument does not think that the truth of the premises definitely establishes the truth of the conclusion, but nonetheless believes that their truth provides good reason to believe the conclusion true, then the argument is inductive.

Lateral thinking is looking at a matter by taking a creative and indirectve approach, by viewing an issue in a new and and unusual light. 

The enemies of reason would be strong emotions and biases mainly. those two things affect an individual's ability to reason.

Sometime Emotional can help reason but in most cases it hinders it. If you want to look at a matter in a reasonable or logical light you should not involve your emotions because sometimes it affects one's ability to rationalize and make exact conclusions on a matter(s). Sometimes emotions works to help us imagine what we should or could do in a situation, that is where lateral thinking comes into place. It varies. If we can justify our emotions in a matter by using solid or tangible evidence then it may be alright in that case/argument.