Yes, don't use that and use the shortcode instead. I just said it was working on my installation so I can't really tell if it's a bug.
<a class="btn" href="[acf field="content_field" post_id="390"]" target="_blank">click</a>
Yes, it should output full image src since it's just a plain text. The same goes on how you created that link, example,
<img src="[acf field="content_field" post_id="390"]">
And it can't fetch alt tag since it's not connected to the media library. The custom field is simply storing the text added to it which happens to be a URL. Hence, the solution would be adding a custom field for image URL, for alt text, and so on. Then use ACF to pull that stored information.