```python
def tile_renders(requests: list, fresh_for: int, size: int) -> list:
    if not isinstance(fresh_for, int) or not isinstance(size, int):
        raise ValueError("fresh_for and size must be positive whole numbers.")
    if fresh_for < 0 or size <= 0:
        raise ValueError("fresh_for and size must be positive whole numbers.")

    cache = {}
    renders = []

    for tick, tile_name in requests:
        if tick < 0:
            raise ValueError("tick cannot be negative.")

        if tick not in cache or tick + fresh_for > cache[tick][0]:
            # Render the tile again
            cache[tick] = (tick + fresh_for, tile_name)
            renders.append([tick, tile_name])
        else:
            # Use the cached render
            renders.append(cache[tick])

        # Maintain the cache size limit
        if len(cache) > size:
            # Drop the oldest render
            oldest_tick = min(cache.keys())
            del cache[oldest_tick]

    return renders
```