Learn Hardcore German: Wir notieren den Abgabetermin fett im Kalender. - We note the submission deadline in bold in the calendar.

notieren – neutral, somewhat formal:
Wir notieren den Abgabetermin im Kalender.
= We note the deadline in the calendar.
aufschreiben – write down, often more everyday/colloquial:
Schreib den Abgabetermin auf.
eintragen – enter / put into a list or form/calendar:
Wir tragen den Abgabetermin in den Kalender ein.
schreiben alone is more general: to write (text, letters, etc.), not specifically “as a note in a calendar”.

What is fett doing in this sentence? Is it an adjective? Why is there no ending?

Here fett means in bold / in boldface / in thick letters.

Grammatically, it’s used as a kind of adverbial describing how we write the date in the calendar:

Wir notieren den Abgabetermin fett im Kalender.
= We write the deadline in bold in the calendar.

There is no adjective ending because it is not directly in front of a noun:

Adjective before noun: ein fetter Termin (a fat/big/thick appointment)
Predicative/adverbial use: Wir schreiben den Termin fett. (We write the date in bold.)

So in this sentence fett is like an adverb: it modifies the way of writing, not the noun itself.

Could I move fett to another position, like Wir notieren fett den Abgabetermin im Kalender?

Yes, German word order is flexible with these adverbials, but the usual and most natural version is:

Other possible orders:

Wir notieren den Abgabetermin im Kalender fett.
(Also okay; sounds slightly more “afterthought style”: “…in the calendar, in bold.”)
Wir notieren fett den Abgabetermin im Kalender.
(Possible, but less common; fett gets more emphasis: “we specifically write it in bold”.)

For standard, neutral style, the given sentence is best.

Why is it im Kalender and not something like in dem Kalender?

im is just the usual contraction of in dem:

So:

Both are grammatically correct, but im Kalender is what people normally say and write.

Why is it im Kalender (dative) and not in den Kalender (accusative)?

The preposition in can take dative (location) or accusative (direction):

In this sentence, im Kalender (in the calendar) describes the place where the information is (its location), not the movement into it:

Wir notieren den Abgabetermin im Kalender.
= We (will) have the deadline in the calendar as a note.

If you want to stress the movement into the calendar, you often use a different verb:

Wir tragen den Abgabetermin in den Kalender ein.
(accusative: in den Kalender – entering it into the calendar)

With notieren, the fixed and most idiomatic phrase is simply etwas im Kalender notieren.

Is the word order Wir notieren den Abgabetermin fett im Kalender the standard German SVO order?

Yes:

So it’s a straightforward S–V–O main clause with extra information at the end, which is typical for German.

Can this German present tense also refer to the future, like English “We’ll note it down”?

Yes. The German Präsens is often used for future meaning when the context is clear:

Wir notieren den Abgabetermin fett im Kalender.
→ Depending on context, this can mean
- We are noting the deadline in bold in the calendar (now).
- We’ll note the deadline in bold in the calendar (later).

If you want to be very explicit about the future, you could also say:

But in everyday speech, the simple present is usually enough.

How else could you express the same idea more colloquially?

Some natural alternatives:

Wir schreiben den Abgabetermin fett in den Kalender.
(Using schreiben and accusative in den Kalender – focusing more on the act of writing it in.)
Wir markieren den Abgabetermin fett im Kalender.
(We mark the deadline in bold in the calendar.)
Wir tragen den Abgabetermin fett in den Kalender ein.
(We enter the deadline in bold into the calendar.)

All keep the idea: you make the deadline stand out visually in the calendar.