How can I tell if this is a gas or wood burning fireplace
That is a wood burning masonry fireplace with a gas log lighter. Gas fireplaces aren't supposed to have dampers, so the damper lets you know that it was originally designed for wood. The log lighter is a convenience to help you light wood fires, if it had fakes logs or a different burner then you would know its a gas fireplace. Its a good idea to get it inspected by a chimney sweep.