der Fall
case
A specific situation, circumstance, or concrete occurrence.
Das ist ein seltener Fall, der nicht oft vorkommt.
That is a rare case that does not occur often.

case / fall
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case
A specific situation, circumstance, or concrete occurrence.
Das ist ein seltener Fall, der nicht oft vorkommt.
That is a rare case that does not occur often.

'Der Fall' does not mean the season autumn/fall. The English word 'fall' (autumn) is called 'der Herbst' in German.
Im Herbst werden die Blätter bunt.
In autumn, the leaves turn colorful.
The noun 'der Fall' is closely related to the verb 'fallen' (to fall). The literal meaning 'Sturz' (fall) as in 'der Fall von der Leiter' (the fall from the ladder) comes directly from this. Other meanings are metaphorical, such as a situation that 'zufällt' (falls to someone / comes someone's way).
Pass auf, dass du auf der nassen Treppe nicht fällst.
Be careful not to fall on the wet stairs.
The many meanings of 'Fall' can be recognized from context. If it is about the police or a crime, it refers to a criminal case. In the context of grammar, it means case. If it is about physical movement, it means a fall.
Der Detektiv übernahm einen neuen Fall.
The detective took on a new case.
The expressions 'auf jeden Fall' (definitely / in any case) and 'auf keinen Fall' (definitely not / under no circumstances) are fixed expressions. They function like adverbs and mean 'absolutely' or 'under no circumstances'.
Ich werde auf jeden Fall zur Party kommen.
I will definitely come to the party.
When 'auf jeden Fall' (definitely / in any case) or 'auf keinen Fall' (definitely not / under no circumstances) appears at the beginning of a sentence (position 1), the conjugated verb follows directly afterward in position 2.
Auf jeden Fall müssen wir heute noch einkaufen.
In any case, we still have to go shopping today.
The expression 'für den Fall, dass' (in case) introduces a subordinate clause. Therefore, the conjugated verb comes at the end of the clause.
Ich gebe dir meine Nummer, für den Fall, dass du Hilfe brauchst.
I'll give you my number in case you need help.
In a legal or police context, 'Fall' is often combined with verbs such as 'einen Fall lösen' (to solve a case), 'einen Fall untersuchen' (to investigate a case), or 'in einem Fall ermitteln' (to investigate in a case).
Die Polizei konnte den komplizierten Fall schnell lösen.
The police were able to solve the complicated case quickly.
if / when
'wenn' and 'für den Fall, dass' both express a condition. 'wenn' is the normal, short form for conditions in everyday language. 'für den Fall, dass' sounds more cautious and emphasizes that you are preparing for a possible situation. It is especially suitable when something might happen and you make a plan in advance. They can be confused because both are often meant as 'if' or 'in case'. In practical terms: use 'wenn' for simple conditions. 'für den Fall, dass' works well for a precaution.

Für den Fall, dass meine Mutter heute länger arbeitet, koche ich das Abendessen.
In case my mother works late today, I'll cook dinner.
Wenn ich heute im Krankenhaus fertig bin, komme ich noch zum Training.
If I finish at the hospital today, I'll still come to training.