Learn Romanian: Îmi pare rău, doamnă!

Literally, it translates to 'It seems bad to me.' Îmi means 'to me', pare means 'seems', and rău means 'bad'. Romanian doesn't use the verb 'to be' for apologizing like English does!

If I want to say 'We are sorry', do I change the verb pare?

No, the verb pare and the word rău stay exactly the same. You only change the person it 'seems bad' to. To say 'we are sorry', you change îmi (to me) to ne (to us), making it Ne pare rău.

Can I use femeie (woman) instead of doamnă here?

No, that would sound very rude! Doamnă is the polite way to address a woman, equivalent to 'madam' or 'ma'am'. Femeie just means 'woman' and isn't used as a polite title.

Why doesn't doamnă have a special ending here, like domnule (sir) does?

When talking directly to a man, you add -ule to make domnule (sir). But for a woman, the polite form doamnă usually stays exactly the same as its dictionary form when you are speaking directly to her.