Wouldn't and won't are not interchangeable in your three sentences. The meanings of the sentences are different depending upon which form of the verb is used.
If wouldn't is replaced by won't in the first sentence, we have:
- Here, you won't say, "May I ask you what is your name?"
Won't (a contraction of will not, the present tense of the verb will with the negative adverb) describes the future from the viewpoint of that future; it describes the future as "its own present." Wouldn't (a contraction of would not, the past tense of the verb will with the negative adverb) describes the future as if viewed from a time further ahead of the present than that future; it describes the future as "its own past."
It is always important to remember that even when the verb will is used as a modal or auxiliary verb, it is not merely a neutral word which places the action in the future. Every use of the verb will also partakes of its original meaning of wish for or want. Thus, wouldn't in your first sentence gives it the meaning:
Looking back at your words as if you had already spoken them, you wish you had not said "May I ask you what is your name?"
This expresses a strong preference for not using those words.
Replacing wouldn't with won't gives the sentence this meaning:
Looking at your words as if you are in the future and speaking them, you do not say "May I ask you what is your name?"
This merely states that, in the future, you do not use those words, with no sense of preference.
The meaning of will as to desire, wish is strong when the past tense would is used, and especially when in the negative as in your sentences. The construction You wouldn't +[bare infinitive] or You wouldn't want +[infinitive] is often used in English to suggest, emphatically, a negative desire or preference:
You wouldn't eat dirt!
You wouldn't want to get a speeding ticket!
‘But you wouldn’t want to read a whole book of text speak,’ I said. (Source)
Another way of saying natural tendency is calling it proclivity, both will and its past equivalent would are used to express, what Michael Swan (Practical English Usage) describes, habits and characteristics
Will and would can be used to talk about repeated and habitual behaviour. Would refers to the past.
- When nobody's looking, she'll go into the kitchen and steal biscuits
- On Sundays, when I was a child, we would get up early and go fishing.
A.J.Thomson A.V.Martinet in their book A Practical English Grammar (4th Ed) explain this nicely, better than I could
Habits in the present are normally expressed by the simple present tense; but will + infinitive can be used instead when we wish to emphasize the characteristics of the performer rather than the action performed. It is chiefly used in general statements:
- An Englishman will usually show you the way in the street (It is normal for an Englishman to act in this way.)
This is not a very important use of will, but the past form, would, has a much wider use and can replace used to when we are describing a past routine.
- On Sundays he used to/would get up early and go fishing. He used to/would spend the whole day by the river and in the evening used to/would come home with marvellous stories of the fish he had nearly caught.
Thus saying that water will boil at 100°C is stating a general characteristic; a natural tendency: the general inclination of water when it is heated at that temperature. Using will in this way is uncommon, but it shows why its past equivalent, would, is often used to express repeated actions in the past. However, would and used to are not always interchangeable.
Examples:
Positive
- Italian middle schools used to teach Latin. = In Italy, Latin was taught at middle school.
- In Italy middle schools would teach Latin. = same meaning as above
BUT in the negative sense
- Italian middle schools didn't use to teach English. = In the past, English was never taught at middle school.
- Italian middle schools wouldn't teach English. = In the past, Italian middle schools refused/did not want to teach English.
In order for wouldn't to convey the same meaning as didn't use to, the adverb never could be employed.
- Italian middle schools would never teach English.
Other examples
As a child I didn't use to wear glasses because I had good eyesight = I didn't wear glasses as a child because my eyesight was good.
As a child I wouldn't wear glasses, although my eyesight was poor. = I refused to wear glasses when I was a child, even if my eyesight was not good. (different meaning)
As a child I would never wear glasses, although my eyesight was poor = similar meaning to 1.
Best Answer
wouldn't isn't only the past tense; it can also be used in a conditional or hypothetical sense.
"I won't even wash my socks in it" is a simple factual statement that I will not do it.
"I wouldn't even wash my socks in it" is essentially saying "I would not use it for anything, even washing my socks." It's like saying "Wash my face in that bathroom? I wouldn't even wash my socks in there" but we don't always say it so verbosely.