Learn Dutch: Ze is weliswaar altijd stipt, maar ze speelt nooit buiten. - She is admittedly always punctual, but she never plays outside.

Weliswaar means admittedly or it is true that, and it pairs with maar (but) to form a correlative structure. It sets up a concession—acknowledging a positive or true fact (ze is altijd stipt)—before delivering a contrasting counter-argument (ze speelt nooit buiten).

Why is weliswaar placed after the verb is? Could I start the sentence with it?

Weliswaar is an adverb, so it normally sits in the middle of the sentence, after the conjugated verb (is). You can start the sentence with it for emphasis, but remember that doing so triggers inversion (putting the verb before the subject): Weliswaar is ze altijd stipt, maar...

Why doesn't the word maar push the verb speelt to the end of the second clause?

Because maar is a coordinating conjunction. Unlike subordinating conjunctions (like hoewel or omdat), coordinating conjunctions just link two main clauses together without affecting the word order of the clause that follows them. The second clause keeps the standard subject-verb order (ze speelt).

Is buiten at the end of the sentence part of a separable verb?