```ts
import { strict as assert } from 'assert';

/**
 * Performs a topological sort on a directed graph represented by nodes and edges.
 * If cycles are detected or invalid edges are present, an error is thrown.
 * 
 * @param nodes - A read-only array of node names.
 * @param edges - A read-only array of tuples representing the [from, to] edges.
 * @returns An ordered array of node names satisfying the edges.
 */
export function topologicalSort(nodes: readonly string[], edges: readonly (readonly [string, string])[]): string[] {
    const graph = new Map<string, Set<string>>();
    
    for (const [from, to] of edges) {
        if (!graph.has(from)) {
            graph.set(from, new Set());
        }
        
        if (!graph.has(to)) {
            graph.set(to, new Set());
        }
        
        graph.get(from)?.add(to);
    }
    
    
    const sorted: string[] = [];
    const inDegree: Map<string, number> = new Map(nodes.map(node => [node, 0]));
    
    for (const node of nodes) {
        if (!inDegree.has(node)) {
            inDegree.set(node, 1);
        }
        
        for (const adjacent of graph.get(node) || []) {
            inDegree.set(adjacent, inDegree.get(adjacent)! - 1);
        }
    }
    
    
    while (sorted.length < nodes.length) {
        let current = null;

        for (const node of nodes) {
            if (!inDegree.has(node)) {
                current = node;
                break;
            }
        }

        if (current === null || !graph.has(current)) {
            throw new Error('Cycle detected or invalid edge');
        }
        
        sorted.push(current);
        inDegree.delete(current);

        for (const adjacent of graph.get(current) || []) {
            inDegree.set(adjacent, inDegree.get(adjacent)! - 1);
        }

    }

    return sorted;
}

// Check function to verify the correctness of the topologicalSort function
function checkTopologicalSort() {
    assert.deepStrictEqual(topologicalSort([], []), [], 'Empty graph should be sorted');
    assert.deepStrictEqual(topologicalSort(['a', 'b'], [['a', 'b']]), ['a', 'b'], 'Single edge with single node');
    assert.deepStrictEqual(topologicalSort(['a', 'b', 'c'], [['a', 'b'], ['b', 'c'], ['c', 'a']]), ['a', 'b', 'c'], 'Circular graph should throw error');
    assert.deepStrictEqual(topologicalSort(['x', 'y', 'z'], [['x', 'y'], ['z', 'x'], ['y', 'z']]), ['y', 'x', 'z'], 'Multi-edge between the same nodes');
    try {
        topologicalSort(['a', 'b', 'c'], [['a', 'd'], ['b', 'e'], ['c', 'f']]);
    } catch (error) {
        assert.equal(error.message, 'Cycle detected or invalid edge', '"a", "d", and "d", and "e" should form a cycle');
    }
    try {
        topologicalSort(['x', 'y'], [['x', 'y']]);
    } catch (error) {
        assert.equal(error.message, 'Invalid edge or nodes missing from graph data structure', '"x" should not be an invalid edge');
    }
}

// Run the check function to verify the solution
checkTopologicalSort();
```