There are different uses of the noun "reason" here.

B,C,D) Are most common, it is a countable noun.

I have reasons for doing this.

Note the use of the plural. This looks very similar to (A) but is using "reason" as a countable noun.

0. Another use of "reason" is an uncountable noun.

There is reason in madness.

A) Example (A) is a phrase "to have reason". Here "reason" means that what you do is reasonable, you could justify it. It is from the uncountable noun. So what you do can be justified.

I have reason to believe you.

I have good reason to do this.

Or you could justify the actions of someone else.

He has reason to do that.

Sometimes, you can justify your expectation of something even if it is not true or provably true,

He has reason to know.

There are different uses of the noun "reason" here.

B,C,D) For these it is a countable noun.

I have reasons for doing this.

Note the use of the plural. This looks very similar to (A) but is using "reason" as a countable noun.

0. Another use of "reason" is an uncountable noun.

There is reason in madness.

A) Example (A) is a phrase "to have reason". Here "reason" means that what you do is reasonable, you could justify it. It is from the uncountable noun. So what you do can be justified.

I have reason to believe you.

I have good reason to do this.

Or you could justify the actions of someone else.

He has reason to do that.

Sometimes, you can justify your expectation of something even if it is not true or provably true,

He has reason to know.