Remove requirement for featured image

I've spent a couple of days customising the template and I am amazed at this situation:

• When I include an image in the excerpt (i.e. before the 'more link' tag) the image does not appear on my blog page of excerpts - instead the 'Continue reading' link is added to the text.
• When I don't include an image in the excerpt then no 'Continue reading' link is added. This is incredible as clearly every excerpt requires a 'read more' link whether or not it contains an image, that is the purpose of an excerpt.
• If I select a featured image in the editor in order to get a 'read more' link then this image does appear in the excerpt but in front of the text.

I would like my excerpts to reflect the posts, i.e. if I have written text and inserted an image then show both and in the order how I created the post. I want to show an image in the correct position if I've included it in the excerpt and then provide a 'read more' link. Could you suggest how to modify the code to create simple excerpts? As a very rough workaround I could post a featured image of a transparent png in order to get the 'read more' link. But I would rather sort out the code...