Teilrechnung

however this might sound as if the invoice is not yet correct or approved...

sounds more appropriate to me

würd ich jetzt sagen.

#4: Gemeint ist wahrscheinlich "intermediate".

I don't think 'intermediate' makes much more sense here than 'intermediary'. This would be a provisional or interim invoice.

I would also vote firmly against both 'intermediate' and 'intermediary.'

'Provisional' might work, but it seems a little odd to me; it could imply that you might change your mind and not ask for payment after all.

'Partial,' 'interim,' and 'preliminary' are all fine, with 'invoice,' 'statement,' 'bill' ...

That's not how I read 'provisional': to me it means an invoice where the final amount has not yet been determined. It could be for part-payment on account, or for 50% payment at the halfway milestone, or something like that.

Partial is OK, but sounds slightly odd; and preliminary is very odd in BE.

A sub-total is can be made on a bill at any time before further items are added - whether these items be goods, services or taxes. Typically the last (oftentimes the only) sub-total will be shown after the addition of goods and services and before the addition of any taxes.

A subtotal before tax is not a Zwischenrechnung.