Learn English – Why do native speakers use “vent your anger” rather than “erase your anger”

You can almost always say "No thank you", which is polite enough on its own, but if you'd like to give a longer response, you could say something like:

No thank you. I appreciate the offer, but I'll be fine on my own.

Sometimes making your reply a little bit longer like this can make you seem more gracious and less brusque.

If you appear to be hurt, it would also be good to say "I'm okay" so they know not to worry.

“That is typical of you” is exactly what “You would!” means in this context. It is listed in some dictionaries, though it can be a little hard to find among the many other meanings of would; for example Cambridge lists it as

would modal verb (FREQUENCY) (…) disapproving used to ​suggest that what ​happens is ​expected because it is ​typical, ​especially of a person's ​behaviour:

"Madeleine called to say she's too ​busy to come." "She would - she always has an ​excuse."

This is closely related to the meaning explained just above: would can express something habitual. For example

He would always ​turn and ​wave at the end of the ​street.

means the same thing as “He always turned and waved …” but the use of would stresses the fact that it's a habit.

As for what you read in Urban Dictionary — don't mistake UD for a useful reference. A lot of what it contains is just what one person decided to add and doesn't mean that anybody else would understand. I, for one (admittedly not a native English speaker), have no idea what why “you would” is supposed to be annoying or this “I did forget”/“but really” business is supposed to mean (maybe it implies that “you would” was used sarcastically?).