Landlords, lenders and agencies often ask for a statement and get a great deal more than they need. You can send exactly what was requested.
A full statement shows every place you shop, every subscription you hold, who you send money to and how much you have. Almost none of that is relevant to proving one payment or one month's income, and once it has been sent you cannot take it back.
Requests are usually more specific than people assume. A deposit check needs the page showing the deposit. Proof of income needs the pages showing salary credits. Sending twelve months because it was easier to download hands over far more than the transaction required.
A statement is also exactly the kind of document that should not be uploaded to an unknown service in order to trim it. The whole reason to trim it is that the contents are sensitive, which makes the trimming tool an odd place to stop caring.
Usually yes, if it shows what was requested. Some institutions require a complete statement and will say so.
The header appears on whichever pages carry it in the original. Check the extract still identifies the account if that is required.
No, and that matters a great deal for this particular document.