Does slå have more definitions?
It's beat in both senses, 'hit' and 'beat' (as in 'win against/versus', obviously the one meant here). It also means strike as in klockan slog två, 'the clock struck two'.
Can it also mean something like "surprise" or "catch off-guard"? At least in a sentence like this one?
Not in a sentence like this one, but there's an expression slå med häpnad which means 'surprise' or 'stun'.
What about slain?
slain is the past participle of slay which means 'slå ihjäl' or 'dräpa' in Swedish.
Sorry, I meant slay. Was just curious if there's a relation, because it sounded similar.
They are the same word historically, yes.
Is slå not of the same root as slutar?
Nope. Sluta is from Low German "Slûten" meaning to close or finish. Slå is from Icelandic "slá" and/or German "schlagen", meaning to hit, and is related to the English "slay".
It's literally impossible to hit her. She has an invisible force field around her at all times.
Ja ingen kan slå våran bot! :D
That's what they said about Ronda Rousey and look at her
In common usage, would it be used as It is impossible to hit her, or would there be a better way of translating that?
This sentence usually means "beat" in the sense of "do better than in competition". I think either "träffa" or "drabba" would work better if you mean "it is impossible to strike her".
Can this mean beat, as it beat in a competition?
That's the most likely meaning in this case.