aufschlagen
to hit
To strike a surface after falling or being thrown, often with a sound.
Der Hagel schlug laut auf das Autodach auf.
The hail hit the car roof loudly.

to open / hit / serve
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to hit
To strike a surface after falling or being thrown, often with a sound.
Der Hagel schlug laut auf das Autodach auf.
The hail hit the car roof loudly.

'Aufschlagen' is a separable verb. The prefix 'auf-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ich schlage schnell das Wörterbuch auf.
I quickly look up the word in the dictionary.
The prefix 'auf-' often means 'open' here. This connects several meanings: you 'schlägt ein Buch auf' (open a book), you 'schlägt ein Ei auf' (crack open an egg), and you 'schlägt sich das Knie auf' (cut your knee open—the skin opens).
Kannst du bitte die Flasche aufschlagen?
Can you please open the bottle?
The object of the verb usually reveals the meaning. A book, a newspaper, or a tent is opened. Eggs or nuts are cracked open. A ball is served in sports. A price is increased. And a person 'schlägt' unexpectedly 'auf' at a place—shows up there.
Wir müssen noch das Zelt für die Nacht aufschlagen.
We still have to pitch the tent for the night.
When something hits after a fall, the surface is often indicated with a preposition such as 'auf' (+ dative) or 'gegen' (+ accusative).
Der Ball schlug hart auf dem Boden auf.
The ball hit the ground hard.
When 'aufschlagen' means that a person appears unexpectedly, this is a colloquial use.
Mein Bruder ist gestern einfach so bei mir aufgeschlagen.
My brother just showed up at my place yesterday.
When you injure yourself, the verb is used reflexively with the dative: 'sich (dative) etwas (accusative) aufschlagen'. The person is in the dative, and the injured body part is in the accusative.
Ich habe mir beim Sport das Kinn aufgeschlagen.
I cut my chin open while playing sports.
When a surcharge is charged, the structure is often: 'einen Betrag (accusative) auf etwas (accusative) aufschlagen' (to add an amount to something).
Wegen der hohen Nachfrage schlug die Fluggesellschaft 50 Euro auf den Ticketpreis auf.
Because of the high demand, the airline added 50 euros to the ticket price.
to appear
'erscheinen' and 'aufschlagen' can both mean that someone arrives at a place or is suddenly there. 'erscheinen' is neutral to formal and fits especially well for appointments, official occasions, or when you want to state objectively that someone is present. 'aufschlagen' in this meaning is colloquial and often sounds surprising or a bit casual. It is used more in conversation among friends when someone suddenly shows up. For authorities, work, or official appointments, 'erscheinen' is usually more natural.

Kurz vor dem Essen schlug Max plötzlich bei uns zu Hause auf.
Shortly before dinner, Max suddenly showed up at our house.
Alle Teilnehmenden müssen pünktlich zum Termin erscheinen.
All participants must appear on time for the appointment.