Ich schicke den Zählerstand noch am selben Tag an die Hausverwaltung.

Because schicken takes a direct object in the accusative case: you send something.

• der Zählerstand = nominative (dictionary form / subject)
• den Zählerstand = accusative (direct object)
• dem Zählerstand = dative (would be used if it were an indirect object, but here it isn’t)

So: Ich schicke den Zählerstand … = I send the meter reading …

Here an is a two-way preposition (can take accusative or dative). With schicken, it typically expresses a direction/target, so it uses the accusative:

• an die Hausverwaltung (accusative) = to the property management (as a destination)
  If it were describing a static location (not a destination), you’d expect dative, e.g. an der Tür = at the door.

• zur Hausverwaltung (= zu der) is often possible and common: Ich schicke den Zählerstand zur Hausverwaltung. It sounds like “to the property management” in a general sense.
• an der Hausverwaltung is generally wrong here, because that would mean something like “at the property management” (a location), not a recipient.

So for sending something: an die Hausverwaltung or zur Hausverwaltung are the typical options.

noch here means something like still / yet / as early as / even depending on context; in this sentence it implies by that same day / on the same day (still)—i.e., it will happen without delay.

Position: noch often sits near the time phrase it modifies:

• … noch am selben Tag … (very natural)
  You could also move it slightly, but the given placement clearly ties it to am selben Tag.

am is a contraction of an dem (dative):

• an dem selben Tag → am selben Tag
  German commonly uses an + dative with days to mean on that day.

Also note the adjective ending: selben is weakly declined because it follows dem (a definite article in dative masculine/neuter).

They’re close, and both are common:

• am selben Tag = on that very/same day (often used when referencing a day already mentioned or clearly implied)
• am gleichen Tag = on the same day (also fine; sometimes feels a bit more neutral/explicit)

In many contexts they are interchangeable, but am selben Tag is especially idiomatic in administrative-style German.

Zählerstand is a compound noun:

• Zähler = meter/counter (e.g., electricity meter, water meter)
• Stand = “state/level/reading” (like “the current value/position”)

So Zählerstand = meter reading (the number shown on the meter).

German main clauses follow the V2 rule: the finite verb (here schicke) is in position 2.

Structure here is straightforward:

1. Ich (subject)
2. schicke (finite verb)
   Then:
   
   • den Zählerstand (direct object)
   • noch am selben Tag (time information)
   • an die Hausverwaltung (recipient/target)

Yes. You can front other elements for emphasis; the verb still stays second:

• Noch am selben Tag schicke ich den Zählerstand an die Hausverwaltung. (emphasizes “the same day”)
• An die Hausverwaltung schicke ich den Zählerstand noch am selben Tag. (emphasizes the recipient)

When you move something to the front, Ich often moves behind the verb: … schicke ich …

More formal (common in emails/letters):

• Ich übermittle den Zählerstand noch am selben Tag an die Hausverwaltung.
• Ich werde den Zählerstand noch am selben Tag an die Hausverwaltung senden.

More informal:

• Ich schicke den Zählerstand noch am selben Tag zur Hausverwaltung.
• Ich schick den Zählerstand noch am selben Tag an die Hausverwaltung. (dropping the -e in speech)