Schloss according to the noun is Castle and verb is to close. Am I correct? Can someone clarify?
Capitalised "Schloss" is a noun: a castle or a lock (as in the thing that you open with a key).
lower-case "schloss" is the past tense of "schließen" = (I, he, she, it) closed
the noun has one more meaning besides castle: it can be a lock as well, which is somewhat closer to the verb schließen.
schloß was correct before the last German orthography reform. Today it has to be schloss.
"Schloss" bears no relationship to the list of "how is the praeteritum formed" verb endings given at the beginning of the exercise. How does it come about?
schließen is a strong verb, so it follows this part of the tips and notes:
The Präteritum of strong verbs is not quite predictable. They usually change the stem and add -st, -en, -t, or no ending at all.
In this case, the changed stem for the past tense is schloss- (the vowel changes from long i(e) to short o) and the ending is no ending at all.
It's similar to how finden gives er fand (with changed stem and no ending).
To lock is abschließen or zuschließen -- those are separable verbs so you might see Er schließt die Tür ab, for example.
But the "lock" meaning comes from the combination of schließt ... ab.
Why not "Er schloss der Tür", isn't Tür receiving an action and it's also feminine therefore needing feminine dative declension "der"?
It's the thing directly affected by the action -- the direct object. Those take the accusative case.
Calling it "receiving action" might be confusing since the recipient of giving is in the dative case (and the thing directly affected by the giving, the given thing, is in the accusative).
He closed the door, swallowed the key, and walked slowly up to Will and Carlton...
I've entered "Er schloss die Tür" 20 times, and each time it says my entry is wrong, and that the correct answer is "Er schloss die Tür," which is exactly what I wrote.
Nearly. Tür is a noun and has to be capitalised, and it has an ü in it, not an u. (Or if you can't make an ü, write it as Tuer.)
But otherwise, Er hat die Tür zugemacht and Er schloss die Tür mean pretty much the same thing.