How to get product image and URL in Magento 2?

This way may not the best way to get a product image.

Inject \Magento\Catalog\Api\ProductRepositoryInterfaceFactory in the constructor.

protected $_productRepositoryFactory;

public function __construct(
 \Magento\Catalog\Api\ProductRepositoryInterfaceFactory $productRepositoryFactory
) {            
    $this->_productRepositoryFactory = $productRepositoryFactory;
}

We can get the image:

$product = $this->_productRepositoryFactory->create()
    ->getById($item->getProductId());
$product->getData('image');
$product->getData('thumbnail');
$product->getData('small_image');

If you need to return a product URL it should look like this:

//todo get product object $product 

$objectManager =\Magento\Framework\App\ObjectManager::getInstance();
$helperImport = $objectManager->get('\Magento\Catalog\Helper\Image');

$imageUrl = $helperImport->init($product, 'product_page_image_small')
                ->setImageFile($product->getSmallImage()) // image,small_image,thumbnail
                ->resize(380)
                ->getUrl();
echo $imageUrl;

If you want the published/cache frontend URL of an image for a specific store view (like I did) this is working for me:

/**
 * @var \Magento\Store\Model\App\Emulation
 */
protected $appEmulation;

/**
 * @var \Magento\Store\Model\StoreManagerInterface
 */
protected $storeManager;

/**
 * @var \Magento\Catalog\Api\ProductRepositoryInterfaceFactory
 */
protected $productRepositoryFactory;

/**
 * @var \Magento\Catalog\Helper\ImageFactory
 */
protected $imageHelperFactory;

/**
 * @param \Magento\Store\Model\StoreManagerInterface $storeManager
 * @param \Magento\Store\Model\App\Emulation $appEmulation
 * @param \Magento\Catalog\Api\ProductRepositoryInterfaceFactory $productRepositoryFactory
 * @param \Magento\Catalog\Helper\ImageFactory $helperFactory
 */
public function __construct(
    \Magento\Store\Model\StoreManagerInterface $storeManager,
    \Magento\Store\Model\App\Emulation $appEmulation,
    \Magento\Catalog\Api\ProductRepositoryInterfaceFactory $productRepositoryFactory,
    \Magento\Catalog\Helper\ImageFactory $imageHelperFactory
)
{
    $this->storeManager = $storeManager;
    $this->appEmulation = $appEmulation;
    $this->productRepositoryFactory = $productRepositoryFactory;
    $this->imageHelperFactory = $imageHelperFactory;
}

Then, wherever you need to get the image frontend URL:

$sku = "my-sku";
// get the store ID from somewhere (maybe a specific store?)
$storeId = $this->storeManager->getStore()->getId();
// emulate the frontend environment
$this->appEmulation->startEnvironmentEmulation($storeId, \Magento\Framework\App\Area::AREA_FRONTEND, true);
// load the product however you want
$product = $this->productRepositoryFactory->create()->get($sku);
// now the image helper will get the correct URL with the frontend environment emulated
$imageUrl = $this->imageHelperFactory->create()
  ->init($product, 'product_thumbnail_image')->getUrl();
// end emulation
$this->appEmulation->stopEnvironmentEmulation();

You can select other images types besides product_thumbnail_image: see magento/theme-frontend-luma/etc/view.xml for a list of available product images, or create your own in a view.xml file.