Learn Dutch: Het parlement steunt de president niet. - Parliament does not support the president.

When negating a sentence with a specific direct object (like de president), niet goes after that object. Since there are no other verbs, prepositional phrases, or adverbs of time to follow it, niet naturally falls at the very end of this clause.

Could I use ondersteunt instead of steunt here?

It is better to use steunt. Steunen is used for political, moral, or financial backing. Ondersteunen usually implies physical support (like a pillar holding up a roof) or practical assistance (like administrative or technical support). Since this is about political backing, steunt is the exact right word.

This lesson is about concessive connectors like niettemin and evenwel. How would I add a second sentence saying 'Nevertheless, he makes the decisions'?

You can use either word, but they often take different positions. You could say: Niettemin neemt hij de beslissingen. (Notice the verb-subject inversion because niettemin is at the start). If you use evenwel, it usually sounds more natural placed after the verb: Hij neemt evenwel de beslissingen.