Learn Swedish: Cykeln är redan låst. - The bicycle is already locked.

You are right that regular adjectives for en-words usually do not add a -t (like en stor cykel). However, låst is a past participle (a verb acting like an adjective). For verbs where the stem ends in an unvoiced consonant (like p, t, k, or s, as in the verb låsa), the base en-word form of the past participle ends in -t. So cykeln är låst is perfectly correct!

If låst is the en-word form, how does it change for ett-words or plural nouns?

Past participles change their endings to match the noun, just like regular adjectives. For an ett-word, it happens to look exactly the same: fönstret är låst (the window is locked). But if the subject is plural, you add an -a: cyklarna är låsta (the bicycles are locked).

Could I put redan at the end of the sentence, like "Cykeln är låst redan"?

It is much more natural to place redan (already) right after the verb (är). In a standard Swedish main clause, sentence adverbs like redan, inte, and ofta normally go in this specific middle position.

Is låst related to the noun for a physical lock?