```python
def tile_renders(requests: list, fresh_for: int, size: int) -> list:
    if not all(isinstance(x, int) for x in requests):
        raise ValueError("All elements of the requests list must be integers.")
    if not isinstance(fresh_for, int) or fresh_for < 0:
        raise ValueError("fresh_for must be a non-negative integer.")
    if not isinstance(size, int) or size <= 0:
        raise ValueError("size must be a positive integer.")

    cache = {}  # Dictionary to hold tile renders: {tick: [name]}
    latest_ticks = {}  # Dictionary to track the latest tick for each tile name

    def add_render(tick, name):
        if name not in cache or tick > latest_ticks[name]:
            if len(cache) >= size:
                oldest_tick = min(latest_ticks.values())
                oldest_name = next(iter(x for x in cache[oldest_tick] if x != name))
                del cache[oldest_tick][cache[oldest_tick].index(oldest_name)]
                print(f"Removing {oldest_name} at tick {oldest_tick} to make room.")
            cache.setdefault(tick, []).append(name)
        latest_ticks[name] = tick

    result = []

    for tick, name in requests:
        if tick < 0:
            raise ValueError("tick cannot be negative.")
        add_render(tick, name)
        result.append([tick, name])

    return result
```