Si l’appareil tombe en panne, garde le ticket de caisse.

Because le becomes l’ before a vowel sound. This is called elision.

So:

• le appareil → l’appareil
• le ami → l’ami
• la école → l’école

French does this to make pronunciation smoother.

Tomber en panne is a very common French expression meaning to break down, to stop working, or to fail.

Literally, tomber means to fall, but in this expression you should learn the whole phrase as a unit:

• La voiture tombe en panne. = The car breaks down.
• Mon téléphone est tombé en panne. = My phone stopped working.

So here, Si l’appareil tombe en panne... means If the device breaks down...

Because French commonly uses si + present tense for a real or possible condition.

Structure:

• Si + present, + present / future / imperative

In this sentence:

• Si l’appareil tombe en panne = if the device breaks down
• garde le ticket de caisse = keep the receipt

So this is normal French:

• Si tu vois Marie, appelle-moi.
• Si tu as faim, mange.

French does not usually use the future after si in this kind of sentence, so Si l’appareil tombera en panne would be wrong here.

Because garde is in the imperative, the form used for commands or instructions.

French imperatives usually do not include the subject pronoun:

• Tu gardes = you keep / you are keeping
• Garde ! = keep!

So:

• Garde le ticket de caisse. = Keep the receipt.

This sentence is giving advice or an instruction to one person.

In the tu form of the imperative, regular -er verbs usually drop the final -s.

Compare:

• Present: tu gardes
• Imperative: garde

More examples:

• tu parles → Parle !
• tu regardes → Regarde !

A famous exception happens before y and en, where the -s often comes back for pronunciation:

• Vas-y !
• Manges-en !

But in your sentence, plain garde is correct.

Ticket de caisse means receipt, especially a receipt from a shop or supermarket.

Literally:

• ticket = slip/ticket
• caisse = checkout, till, cash register

So the whole phrase is basically checkout receipt.

In everyday French in France, ticket de caisse is a very common expression for the proof of purchase you get in a store.

Because it refers to the specific receipt connected with that purchase.

Here, le means something like the relevant receipt or the receipt for that item. French often uses the definite article when the object is understood from the situation.

So garde le ticket de caisse means:

• keep the receipt
• meaning the receipt you got when you bought the device

Using un ticket de caisse would sound less natural here, because the speaker is not talking about just any receipt.

Yes, you could, but the meaning shifts slightly.

• tomber en panne = to break down, to stop working
  This focuses on the moment or event of failure.
• être en panne = to be broken down, to be out of order
  This focuses on the state.

So:

• Si l’appareil tombe en panne... = If the device breaks down...
• Si l’appareil est en panne... = If the device is broken / is not working...

Both are possible, but tomber en panne is especially natural when talking about something going wrong.

Si means if.

It introduces the condition:

• Si l’appareil tombe en panne = If the device breaks down

This is one of the most basic and common uses of si in French.

Be careful not to confuse it with:

• si = if
• oui = yes

Also, French has another si meaning yes in reply to a negative question, but that is a different use.

It is normal and natural to use a comma when the si clause comes first.

So this is standard:

• Si l’appareil tombe en panne, garde le ticket de caisse.

If you reverse the order, the comma is often omitted:

• Garde le ticket de caisse si l’appareil tombe en panne.

So the comma here helps separate the condition from the main instruction.