I am not familiar with this usage of steht. Is "Das Kleid passt dir" also acceptable?
No. When "es passt dir" it is translated as it "it suits you". For example: "Lass uns um 18 Uhr treffen. Passt dir?" It's like ... is it ok with you? Informal usage is "Das passt." - "That suits me". "stehen" is usually used for clothes. However, you are allowed to say "Das Kleid passt dir gut". Normally it comes with an adjective, but stehen is the traditional use. Passen here sounds good, but people would look at you strangely.
I have to disagree a little. "Es passt dir" can mean "it fits" sizewise (and ,as you said, appointments and plans), whereas "es passt zu dir" = "es steht dir" means "it suits you" from the style, colour etc.
On hover over word "steht" it says "steht dir" = fits you well.
Shouldn't "steht dir gut" = fits you well ?
You can say "steht dir gut", but it is not necessary just like you can say "suits you" instead of "suits you well".
I think "steht dir" becomes "suits you". theres no need for a well or good.
I said that dress becomes you and it was not accepted. I believe it means the same thing as suits you. (?)
Unfortunately it could also mean that the dress magically transforms into you. Not every expression is accepted and in this case they are trying to make sure you understand the German expression.
When it means "to stand", it is intransitive (there is no object). "dir" in object position automatically lets us know that this is one of those special verbs in which the direct object becomes the subject and the person who would with another verb be the subject becomes the indirect object.
Some verbs decide that object is dative. The ones that come to mind: "helfen, folgen, danken" and apparently "stehen" when it means "to suit".