Learn Hardcore German: Mit deiner Mithilfe und einer klaren Absprache schaffen wir die Gruppenarbeit rechtzeitig. - With your assistance and a clear arrangement we will finish the group work in time.

Nominative: eine klare Absprache
(Eine klare Absprache ist wichtig.)
Dative: einer klaren Absprache
(Mit einer klaren Absprache ist alles einfacher.)

So:

mit → dative
feminine singular dative → einer klaren Absprache

What’s the difference between Mithilfe and Hilfe?

Both relate to help, but there’s a nuance:

Hilfe = help in general
- mit deiner Hilfe = with your help
Mithilfe = cooperation/assistance, often with the idea that you are actively joining in
- mit deiner Mithilfe = with your active help / with your assistance

In this sentence, Mit deiner Mithilfe emphasizes that the person is actively involved, not just passively helping in the background.

You could also say:

Mit deiner Hilfe und einer klaren Absprache schaffen wir die Gruppenarbeit rechtzeitig.

That would be perfectly correct; it’s just a bit more neutral.

What exactly does Absprache mean here?

Absprache means something like:

prior agreement,
coordination,
clear arrangement about who does what, when, and how.

It’s related to the verb absprechen (to agree on something, to coordinate).

So eine klare Absprache is:

a clear agreement or coordination between the people in the group
so that everyone knows their tasks and expectations

Rough synonyms in German: Vereinbarung, Abmachung, Klärung, Abstimmung.

Why does the verb schaffen come after the long phrase Mit deiner Mithilfe und einer klaren Absprache?

Because German main clauses follow the verb-second rule (V2-Regel):

The conjugated verb must be in second position in the sentence.

The first “position” can be:

the subject, or
any other element (time, place, prepositional phrase, etc.)

Here:

Mit deiner Mithilfe und einer klaren Absprache = first element
schaffen (the verb) = second element
wir die Gruppenarbeit rechtzeitig = rest of the sentence

So the structure is:

[Mit deiner Mithilfe und einer klaren Absprache] [schaffen] [wir die Gruppenarbeit rechtzeitig].

If you start with Wir, the verb still stays in second position:

Wir schaffen die Gruppenarbeit mit deiner Mithilfe und einer klaren Absprache rechtzeitig.

Can I also say Wir schaffen die Gruppenarbeit mit deiner Mithilfe und einer klaren Absprache rechtzeitig?

Yes, that sentence is completely correct and natural.

Differences in emphasis:

Mit deiner Mithilfe und einer klaren Absprache schaffen wir …
→ puts more emphasis on the conditions (with your help and clear coordination)
Wir schaffen die Gruppenarbeit mit deiner Mithilfe und einer klaren Absprache rechtzeitig.
→ starts by emphasizing we (we will manage it), and then adds the conditions

Both are fine; the choice is mostly stylistic.

What does schaffen mean in this sentence, and how is it different from machen or erstellen?

Here schaffen means:

to manage (to do something in time)
to succeed in completing something

So:

Wir schaffen die Gruppenarbeit rechtzeitig.
= We will manage to complete the group work in time.

Differences:

machen = to do/make (very general)
- Wir machen die Gruppenarbeit. = We do the group work.
erstellen = to create/compile (often used for documents, reports, lists)
- Wir erstellen den Bericht. = We are creating the report.
schaffen (in this sense) = to get something done / accomplish it, often with a sense of effort or time pressure
- Schaffen wir das bis morgen? = Can we manage that by tomorrow?

Note: schaffen can also mean to create (e.g. Gott schuf die Welt), but in everyday speech, especially with time expressions (rechtzeitig, bis morgen, etc.), it usually means to manage / to get done.

What case is die Gruppenarbeit, and how can I tell?

die Gruppenarbeit is in the accusative case as the direct object of schaffen.

Verb: schaffen (to manage/complete something)
Object: Was schaffen wir? – die Gruppenarbeit
→ direct object → accusative

For feminine nouns like Gruppenarbeit, the definite article die is the same in nominative and accusative singular:

Nominative: die Gruppenarbeit (Die Gruppenarbeit ist schwierig.)
Accusative: die Gruppenarbeit (Wir schaffen die Gruppenarbeit.)

So you recognize the case here more from the sentence structure (verb + direct object) than from a change in the article form.

What does rechtzeitig mean exactly? Is it the same as pünktlich?

rechtzeitig means:

in time, early enough, before the deadline, before it’s too late.

pünktlich means:

on time, punctual, exactly at the agreed time.

In this sentence:

rechtzeitig → they will finish the group work before the deadline, with enough time.

Examples:

rechtzeitig ankommen = arrive in time (not too late)
pünktlich um 8 Uhr ankommen = arrive exactly at 8 o’clock

Sometimes they overlap in meaning, but:

rechtzeitig stresses not too late
pünktlich stresses exactly at the agreed time

Why are Mithilfe, Absprache, and Gruppenarbeit capitalized?

Because in German all nouns are capitalized.

Mithilfe – a noun meaning “help/assistance”
Absprache – a noun meaning “agreement/coordination”
Gruppenarbeit – a compound noun: Gruppe
- Arbeit = “group work”

Even when they come after prepositions or in the middle of the sentence, nouns stay capitalized:

mit deiner Mithilfe
einer klaren Absprache
die Gruppenarbeit

Could I use dank deiner Mithilfe instead of mit deiner Mithilfe?

Yes, you could say:

Dank deiner Mithilfe und einer klaren Absprache schaffen wir die Gruppenarbeit rechtzeitig.

The meaning is very close, but the nuance changes slightly:

mit deiner Mithilfe = with your help (your help is one of the conditions/tools)
dank deiner Mithilfe = thanks to your help (your help is the reason we manage it)

So dank emphasizes gratitude/causality a bit more than mit.

Is Gruppenarbeit always about school or university group work?

Most commonly, Gruppenarbeit refers to:

group work in school, university, or training courses
(students or participants work together on a task)

But it can also be used more generally for:

work done in a group/team in other contexts (courses, workshops, sometimes workplaces)

Grammar info:

Gender: die Gruppenarbeit (feminine)
Plural: die Gruppenarbeiten

Examples:

Wir machen heute Gruppenarbeit im Unterricht.
Die Gruppenarbeit wird am Freitag abgegeben.