Learn English – make the house look/looks(?) more beautiful

In this case, wish is semantically but not grammatically correct. Hope is the correct answer.

You can absolutely wish that something wouldn't happen in the future. This conveys a meaning very similar to hope, but suggests that you think the desired negative circumstance (e.g. not raining) is rather unlikely.

In the example, wish is not correct, because I wish it doesn't rain is ungrammatical. You should use wouldn't with wish when talking about future circumstances. Couldn't also works, if you're wishing for a denial of any capability, but that doesn't make much sense when talking about weather.

Here's an example of a common usage of wishing for something negative:

I wish you wouldn't do that.

This is said to someone exhibiting some habitual and unpleasant behavior as a polite way of asking them to stop doing it, both now and in the future.

"I do not" is an expression of fact, or personal observation. "I will not" describes a personal preference. In this case, it's more common to express this as a preference, so either C or D ("won't accept") is better.

I think it's a question of context and dialect whether "excuse" should be singular or plural, so I can't say for certain which would be better. Personally, I would have said:

I won't accept any excuses.

"Do not" is more common when speaking for some third party, either because they are an organization which has no "preference" as such:

The Home Office does not accept any excuses for tardiness.

or because it sounds better to describe what you have observed, rather than assuming someone else's preference:

I would accept your reason for being late, but the President is an impatient man who does not normally tolerate any excuses. You have to try harder next time.

"Do not" is also fine if you want to express a personal preference as if it was an immutable fact:

I do not accept excuses for tardiness. Be here on time, or don't bother to come in at all.