[British English = BrE / American English = AmE]

"In British English there are two separate verbs Need.
Need as a main verb has the question form Do you need?, the negative You don't need and the past forms Needed, Did you need? and Didn't need. It has two meanings: 1. To require something or to think that something is necessary: Do you need any help? *I needed to get some sleep. 2. To have to or to be obliged to do something: Will we need to show our passports?

Need as a modal verb has need for all forms of the present tense, Need you? as the question form and Need not (needn't) as the negative. The past is Need have, Needn't have. It is used to say that something is or is not necessary: Need I pay the whole amount now?

In American English only the main verb is used. This leads to some important differences in the use and meaning of need in British and American English.
In American English it is more common for Need to be used to speak about what is necessary, rather than about what you must do: I don't need to go home yet - it's still early. (BrE and AmE = it isn't necessary) *You don't need to go home yet - we never go to bed before midnight. (BrE = you don't have to.)
The difference is even more noticeable in the past tenses: He didn't need to go to hospital, but he went just to reassure himself. (AmE) *He needn't have gone to hospital, but he went just to reassure himself. (BrE = he did something that wasn't necessary.) *He didn't need to go to hospital after all - he only had a few bruises. (BrE= he didn't go.)”

["ETYMOLOGY: Middle English oughte (1st & 3d singular present indicative), from oughte, 1st & 3d singular past indicative & subjunctive of owen to own"]

["We use ought to have + V3 form to talk about things that were desired or ideal in the past but which didn't happen. It can express regret."]

["The negative form of ought to is ought not to, which is sometimes shortened to oughtn't to in spoken English."]

["The standard construction for the negative is he ought not to have gone: the forms he didn't ought to have gone and he hadn't ought to have gone are not acceptable in standard modern English."]

Would you come in here a moment?

Would you go with me?

Would you shut the window, please?

Would someone please tell me what is going on?

# "You use would, usually in questions with 'like', when you are making a polite offer or invitation."

Would you like a coffee?

# "Would is used in auxiliary function to express repeated, custom or habitual action, event or behaviour in past: used to. PAST HABITS: used to say that something happened often or regularly in the past."

She would sit for hours at the window.

We would meet often for lunch.

Note: "I would think / I would imagine / I would say: Spoken - Used to give your opinion about something when you are not very sure about it:

I would think you'd be happier in a different school.

'Will it cost a lot?' 'I would imagine so.'"