Learn German: Arbeitet Ihre Mutter heute? - Is your mother working today?

The word Ihr is the formal version of 'your'. We add an -e to the end to make it Ihre because the noun it belongs to, Mutter (mother), is feminine and acts as the subject of the sentence.

Would it mean something else if Ihre was written with a lowercase i?

Yes! The capitalized Ihre always means the formal 'your'. If it were written with a lowercase i (ihre), it would mean 'her' or 'their'. Capitalizing the formal version is how we tell them apart in writing.

Why is there an extra 'e' in arbeitet? Shouldn't the ending just be '-t'?

The root of the verb arbeiten (to work) is arbeit-. Because the root ends in a 't', adding the normal -t ending for 'she' would make it hard to pronounce (arbeitt). To fix this, German adds a connecting -e- to make it arbeitet.

Why isn't there a word for 'Is' or 'Does' at the beginning of the German sentence?

German doesn't use helper verbs like 'is' or 'does' to ask questions. Instead of saying 'Is your mother working?', you simply put the main verb first. The sentence literally translates to 'Works your mother today?'.