Eine Mücke sticht mich immer dann, wenn ich keine Jacke trage.

Because Mücke is a feminine noun in German: die Mücke.

In the nominative singular, the indefinite article for feminine nouns is eine:

• eine Mücke = a mosquito

So the subject of the sentence is eine Mücke.

Sticht is the 3rd person singular form of the verb stechen.

The subject is eine Mücke, which is grammatically singular, so the verb must also be singular:

• ich steche
• du stichst
• er/sie/es sticht
• wir stechen
• ihr stecht
• sie stechen

So:

• Eine Mücke sticht mich = A mosquito bites/stings me

Also note that stechen is a strong verb, so the stem vowel changes from e to i in some forms, including er/sie/es sticht.

Because stechen takes a direct object in the accusative case.

So:

• jemanden stechen = to bite/sting someone

That gives:

• mich = accusative of ich
• mir = dative of ich

In this sentence, the mosquito is directly acting on me, so German uses the accusative:

• Eine Mücke sticht mich

Not:

• Eine Mücke sticht mir

Immer dann, wenn means something like:

• whenever
• every time that
• always when

It is a more explicit, slightly fuller way of expressing repeated situations.

So:

• wenn ich keine Jacke trage = when I’m not wearing a jacket
• immer dann, wenn ich keine Jacke trage = whenever I’m not wearing a jacket

You could often replace it with just wenn, but immer dann, wenn emphasizes that this happens repeatedly.

Because wenn introduces a subordinate clause, and in German subordinate clauses the conjugated verb goes to the end.

Main clause:

• Eine Mücke sticht mich

Subordinate clause:

• wenn ich keine Jacke trage

That final position of trage is completely normal after wenn.

Because Jacke is feminine, and here it is the direct object of trage.

The negative article kein changes like ein and agrees with the noun in gender, number, and case.

Since Jacke is feminine singular and in the accusative, you get:

• keine Jacke = no jacket / not wearing a jacket

Compare:

• kein Mantel = no coat
• keine Jacke = no jacket
• kein Hemd = no shirt
• keine Schuhe = no shoes

Because eine Jacke tragen is the normal German way to say to wear a jacket.

So:

• ich trage eine Jacke = I am wearing a jacket
• ich trage keine Jacke = I am not wearing a jacket

German often uses tragen for clothes, glasses, jewelry, and similar things.

Yes, very often.

You could say:

• Eine Mücke sticht mich immer dann, wenn ich keine Jacke anhabe.

That also means A mosquito bites me whenever I’m not wearing a jacket.

Very roughly:

• tragen = to wear
• anhaben = to have on

In everyday speech, anhaben is extremely common for clothing. Tragen is also completely correct and natural.

Because immer dann is still part of the main clause.

The comma comes before the subordinate clause introduced by wenn:

• Eine Mücke sticht mich immer dann, wenn ich keine Jacke trage.

So the structure is:

• main clause: Eine Mücke sticht mich immer dann
• subordinate clause: wenn ich keine Jacke trage

German requires a comma before subordinate clauses like those introduced by wenn, dass, weil, and so on.

Yes. German allows that very naturally:

• Wenn ich keine Jacke trage, sticht mich immer dann eine Mücke.

But that version sounds a bit less natural because immer dann fits most smoothly with wenn.

A more natural fronted version would be:

• Immer dann, wenn ich keine Jacke trage, sticht mich eine Mücke.

When the subordinate clause or adverbial phrase comes first, the main clause still follows the verb-second rule, so you get:

• ..., sticht mich eine Mücke not
• ..., eine Mücke sticht mich

German often uses the singular indefinite article to describe something that typically happens:

• Eine Mücke sticht mich ... = A mosquito bites me ...

This does not necessarily mean the exact same single mosquito every time. It can express a general recurring event.

German could also use the plural in some contexts, but the singular here is very normal and idiomatic.

Yes. For insects like mosquitoes, stechen is the standard verb in German.

German distinguishes between:

• beißen = to bite
• stechen = to sting / to bite in the insect sense used for mosquitoes, wasps, bees, etc.

So although English usually says mosquitoes bite, German says:

• Mücken stechen

That is one of those places where the most natural verb differs between the two languages.