is it valid to say "mind _to do something_"?

Mind in the UK typically means both 'do you care if' and 'be careful of' So 'Mind the stairs' or 'Mind the oven' means 'Be careful of the stairs' or 'be careful of the oven' For your phrase to mean 'Do you care if you climb from the bottom?' you would have to say ' Do you mind climbing from the bottom?' In some parts of the UK (Scotland definitely but maybe other places too) 'mind' has a third meaning. It means 'remember' So 'Do you mind climbing from the bottom?' or 'Mind climbing from the bottom?' can also mean 'Do you remember climbing from the bottom?' and 'mind the milk' means 'remember to get milk' It is only in context that you can tell what the meaning of the sentence is.

It can be used to politely ask someone to do/allow something minor “Mind if I sit here?” “Would you mind babysitting tomorrow?” It would sound a bit hostile if you don’t request something - though still a fairly polite way to express upset. For example: your child is playing music really loudly. Polite request: “Mind turning the volume down?” More hostile version: “Do you mind?!”

There's a rarer more colloquial term (I think it's southern USA origin?) That goes "I've a mind to [do something]" usually to show you're close to doing something out of frustration . For example: "I've a mind to go tell my boss a thing or two!" Meaning: I'm really close to going over and yelling at my boss. Lol However, this is a more regional phrase I think, so depending on where you use it, people may be confused.

Well "mind climbing from the bottom?" doesn't mean what you want it to mean, no. As a phrase "mind climbing from the bottom" as a statement, not a question, would be a use of 'mind' as a shortening of 'mind yourself', telling someone to 'watch out'. ie. it would be "mind yourself climbing from the bottom" and imply you had spotted something tricky about climbing (up?) from the bottom (of something) and are asking them to be careful.

No. "Mind your own business" is an idiomatic phrase, and it's a command. There are a few others - "Mind your language" (ie don't swear), "Mind your manners" (behave appropriately), "Mind how you go" (take care, said when saying goodbye), and so on. For those other phrases to work, you'd need to ask "Do you mind...".

Yeah, it doesn't sound aggressive at all. Quite the contrary: it sounds like you're politely asking someone to climb from the bottom.

Mind never means "do you want you" In "Mind your own business" it means "Take care of" or "Pay attention to" your own business. "Mind climbing from the bottom?" would mean "Do you mind...", which really means "Would you please..." or "would it bother you to..."

Do you mind explaining what you’re talking about? 😉 That’s about how you’d do it.

Mind the gap- be aware there is a gap there, don't fall. Do you mind...- does it bother you if

related: in Scotland you'll hear "Mind and take your umbrella in case it rains"; mind meaning remember.

This is fine to say in the correct context, if you have a friendly demeanor and disposition while you say it, it will be taken perfectly acceptable, however, if you don't the wording could be considered passive-aggressive. You are also cutting off the beginning for expediency however, as the full phrase would be "**Do you** mind climbing from the bottom?" which would make it significantly more innocuous.

I think that works, yes. It would be short for 'Do/would you mind \[x\]?' This one is tricky, because this can *sometimes* be a bit rude or insulting. This isn't always the case, and might depend on the tone of your voice and the context. Literally, 'do you mind' is asking if it would inconvenience them. But I think that sometimes it is used sarcastically, where we actually don't care if it is inconvenient, but they should do it anyway. So I'd be careful about using it. I'm trying to think of a general rule for the contexts where it might sound rude, and I think it is hard to describe it.