Grammar question about articles.

Usage of articles with conjunctions “and” and “or”.

I am pondering over the usage of articles with conjunctions. As far as I know, if the things we are talking about are two different things, use separate articles before each word/noun. For instance:

Mr. Cook bought us a cup of tea and a cup of coffee.

On the other hand, if these two things are a part of something, use only one article before the two words/nouns. Also, it takes singular verb (subject and verb agreement.)

For instance,

A horse and his hair is long.

I find it difficult when to use only one article before and when to use two articles.

Examples:

A username and password is required in order to log in to the website.
VS
A username and a password are required in order to log in to the website.

Similarly, with “or”

Is it a good or a bad thing VS Is it a good or bad thing.

Anyone know how to use articles in these cases? Are there any websites that can help me understand the usage?