Hero block (image) height

It's down to the layout you are using. You need to use a full width layout for the home page if that's where the hero block needs to be. Have a look at https://holisticwebservices.com - is this the type of display you are looking for? Which layout are you using and what theme?  

The Hero block height is determined by the content inside the block. Hero blocks are not the best option to display images. A hero is by definition a large text block that has a decorative background image.

You have a few options (I'm no expert on front end, so there may be better ones)

• You could use hero block with an image and without text, and then add css classes to the block (under "style options"). Then use custom css rules to achieve the height you want (or an auto height)
• You can create a flexible layout template, with a region devoted to showing the image, then create a layout that uses it, put a custom block (or field block) with the image in it,  and use custom css rules to achieve what you want.
• Or, you can edit the template file for a specific layout, and hard code some markup there to show the image, combined with some css

People tend to use CSS Injector to add custom css rules to sites.

Instead of using the Hero block, I would use a standard custom block to insert an image - alone or together with text.

When I make a custom block via admin/structure/block/add, the process is complicated by the fact that the field for creating a new block lacks a CKE editor or some other editor to facilitate writing code (for example, I use BUEditor to create pages, CKEditor and IMCE but they don't work in the create new block field or at least I don't know how to get them to work. If anyone can help me how to enable these editors in the custom block creation form I would appreciate it.

Therefore, I use a trick - I write the content of the custom block as a regular page (in which I am facilitated by the presence of the editors mentioned above), and then I copy the code into the desired custom block with an image.

I find this way much more versatile and it simplifies the structure of the site, having a Hero block seems to me an unnecessary complication to the development and architecture of the site.

Adding a specific CSS style for the custom block as argiepiano pointed out works for any custom block and makes it even easier to make an image block especially in combination with the CSS Injector module or by managing the CSS style through the styles in the site's theme.

This allows for a maximum set of tools for image and text placement, size and composition in this block.

Using nivo-slider or another slider module, eg flexslider also solves the problem, but it is an unnecessary burden on the code page if only one image will be displayed in that block.

Once a custom block is created, it is positioned on the page by editing its layout and placing it in the desired region.