Learn Dutch: Ik zag dat de bruid zich over de vlek opwond. - I saw that the bride got worked up about the stain.

In subordinate clauses, the subject comes right after the conjunction (dat). Because the subject here is a full noun (de bruid) rather than a pronoun, the reflexive pronoun zich cannot jump ahead of it. It must sit strictly after the subject. Saying '...dat zich de bruid...' is grammatically incorrect.

What is the infinitive of opwond and why is it written as one word here?

The infinitive is zich opwinden (to get worked up or agitated). It is a separable verb (op + winden). In a main clause, the prefix splits off and goes to the end. However, because this is a subordinate clause, all verb parts move to the end. When a separable verb is pushed to the end of a clause like this, its prefix and verb reattach to form a single word: opwond.

Could I place over de vlek after the verb opwond?

Yes, you can. Because over de vlek is a prepositional phrase, it is allowed to break the standard rule of verbs going at the very end of a subordinate clause. You could say '...dat de bruid zich opwond over de vlek'. Both word orders are perfectly natural.

Could I place over de vlek before zich?