Learn Hardcore German: Hast du Fragen zur Hausarbeit, komm einfach in meine Lerngruppe. - If you have questions about the term paper, just come to my study group.

Statement: Du hast Fragen zur Hausarbeit. – You have questions about the assignment.
Question: Hast du Fragen zur Hausarbeit? – Do you have questions about the assignment?

So Hast du is just the normal inversion used to turn a statement into a question, just like English You are → Are you.

Should there be a question mark after Hausarbeit instead of a comma?

In careful written German, yes, this would usually be separated into two sentences:

Hast du Fragen zur Hausarbeit? Komm einfach in meine Lerngruppe.

With a question mark, the first part is clearly a question, and the second part is an imperative sentence.

Writing it with a comma as:

Hast du Fragen zur Hausarbeit, komm einfach in meine Lerngruppe.

is common in informal writing (texts, emails, notes), but it is technically a bit sloppy because it splices a question and a main clause with just a comma. In spoken language, this structure is completely normal.

What exactly does zur mean in zur Hausarbeit, and why not zu die Hausarbeit?

Zur is a contraction of zu der:

zu = to, about, concerning
der = dative feminine singular article for many feminine nouns

Hausarbeit is grammatically feminine (die Hausarbeit). After zu, you need the dative case:

zu der Hausarbeit (dative feminine)
→ contracted to zur Hausarbeit

So:

zu die Hausarbeit is wrong (mixing preposition + accusative article).
Correct: zur Hausarbeit (zu der Hausarbeit).

Does Hausarbeit mean “homework” or “housework” here?

It can mean several things depending on context:

School context (especially university):
- Hausarbeit = an academic paper / term paper / written assignment.
- Example: writing a 10‑page essay for a seminar.
General school context (sometimes):
- Hausaufgaben is the usual word for “homework”.
- But people may loosely refer to written assignments as Hausarbeit.
Household context:
- Hausarbeit can also mean “housework” (cleaning, cooking, etc.), but then the rest of the context usually makes that clear.

In your sentence, Lerngruppe (study group) suggests it’s about a school or university written assignment / homework, not cleaning the house.

Why is it komm and not kommst or komme?

Komm is the imperative form for du (informal singular “you”):

Infinitive: kommen – to come
du-form (present): du kommst
Imperative (telling one person informally to do something): komm!

So:

Komm einfach in meine Lerngruppe. – Just come to my study group.

You do not use kommst in the imperative; kommst is used in statements or questions:

Du kommst in meine Lerngruppe.
Kommst du in meine Lerngruppe?

What does einfach add to the meaning? Is it necessary?

Einfach here is not really “simple” in the literal sense; it functions more like a softening particle:

Komm in meine Lerngruppe. – Come to my study group. (quite direct)
Komm einfach in meine Lerngruppe. – Just come to my study group. / Feel free to come…

It makes the invitation sound more relaxed and friendly, not like a command. It’s very common in spoken German.

It’s not grammatically necessary; you could leave it out, but you would lose that softening nuance.

What is a Lerngruppe exactly?

A Lerngruppe is a study group:

A small group of students who meet to study together, do homework, prepare for exams, or discuss course material.
It is usually informal and organized by students themselves (not an official class taught by a teacher), though sometimes teachers encourage them.

So meine Lerngruppe is likely “the study group I organize / attend”.

Could you also say Wenn du Fragen zur Hausarbeit hast, komm einfach in meine Lerngruppe? Is there any difference?

Yes, that version is fully correct and slightly more formal:

Wenn du Fragen zur Hausarbeit hast, komm einfach in meine Lerngruppe.

Here:

wenn = if/when
The verb hast goes to the end of the wenn‑clause, as required for subordinate clauses in German:
- wenn
  - subject + … + verb (final)

This structure is textbook‑correct and sounds neutral or slightly more formal.

Your original:

Hast du Fragen zur Hausarbeit, komm einfach in meine Lerngruppe.

is more colloquial and is something you’d often hear in spoken German. It essentially means the same thing as the wenn‑version, just with a more conversational flavor.

Why is Fragen plural? Could I say eine Frage instead?

You can use either, but they mean slightly different things:

Hast du Fragen zur Hausarbeit …
Literally: Do you have questions about the assignment…?
This is a standard way to invite any kind of questions (one or more). In German, using the plural here is very common and idiomatic.
Hast du eine Frage zur Hausarbeit …
Literally: Do you have a question about the assignment…?
This focuses on the idea of a single question and sounds a bit more specific.

In practice, Hast du Fragen … is the more typical wording for a general invitation to ask anything.

Why is it meine Lerngruppe and not something like zu meiner Lerngruppe or in der Lerngruppe?

The verb kommen often goes with different prepositions, each giving a slightly different nuance:

in meine Lerngruppe kommen
– to come into my study group / to join my study group
(movement into the group; accusative: meine Lerngruppe)
zu meiner Lerngruppe kommen
– to come to my study group (meeting/place)
(movement towards a place or event; dative: meiner Lerngruppe)

In your sentence:

Komm einfach in meine Lerngruppe.

suggests joining or taking part in the study group, not just physically going to where it takes place. It’s like “join my study group” rather than just “come to where my study group meets”.

Both in meine Lerngruppe and zu meiner Lerngruppe can be grammatically correct, but they highlight slightly different aspects (joining the group vs going to the meeting).

Is this sentence formal or informal? Could I use it with my professor or with strangers?

It is informal because it uses du:

Hast du Fragen …, komm … – Do you (informal, singular) have questions …, come …

You would use this:

with friends
with classmates
as a teacher speaking informally to children or to people you’re on du terms with

To say this formally to, say, a professor or someone you address with Sie, you would need:

Haben Sie Fragen zur Hausarbeit, kommen Sie einfach in meine Lerngruppe.

So: the given sentence is not appropriate in a formal context where Sie is expected.