Learn Swedish: Har han fixat cykeln själv? - Has he fixed the bicycle himself?

The word for oneself changes to match the subject it refers to. Here, the subject is han (he), which takes the basic singular form själv. If the subject were plural, like de (they), you would use själva. If it were a singular ett-word like barnet (the child), you would use självt.

Could I put själv earlier in the sentence, like right after han?

In Swedish, when själv means that the subject did something without help, it usually goes at the end of the clause, after the object (cykeln). Putting it right after the subject is sometimes possible for heavy emphasis, but placing it at the end is the most natural and common word order.

Why is the bicycle spelled cykeln and not cykelen?

The base word is en cykel. For nouns ending in -el, -er, or -en, Swedish usually drops the extra e before adding the definite ending to make them easier to pronounce. So, cykel plus the definite ending shrinks down to cykeln.

Is fixat the simple past tense of fixa?