Sorry to hear you are having issues with the plugin, i will do my best to help you and get these issues resolved quickly.
If possible, would you be able to send me a screenshot of your settings for each section of the importer, and a copy of the file you are using so i can best understand what is going wrong.
What type of file are you importing (csv, or xml)?
Are you running on a single or multisite install?
I will try and answer your email in order:
Where do the custom fields come from. I added custom fields in Wordpress and with a plugin. Neither were available on the import page.
The custom field list within the importer is only populated when using plugins such as 'advanced custom fields' and 'yoast' (popular plugins that i have manually created integrations for). You can bypass the dropdown by checking the 'enable text field' to manually enter the custom field key.
I have attached a file i have just created that will list all custom fields that it finds in the database per user, post_type, taxonomies. This will require that you have created a demo record (e.g. a post, page or whatever you are importing with values set for each custom field that you want to import), this will make sure the custom fields are stored in the database and can be found and populate the dropdown under the heading "Generic Custom Fields". To use the attached field, add it to your your /wp-content/mu-plugins folder.
The author field does not work. It only imports the first author - same author for all posts. Does not match authors. This is the most important field for me so I can match the posts with the author.
I have tested this by enabling the author field on posts under the settings tab and testing all the author field types ( ID, Login, Email) and it appears, can you confirm that for the posts that the author is missing that the user/author exists on the system?
Are you able to send me a screenshot of your importer author settings? and is it possible for you to send me the file you are trying to import so i can test it out?
Suggestion: I have to create an excerpt. It should be able to copy in a specified number of characters from the content/description field as the excerpt.
The excerpt field is not required, if you leave it blank it should do what you are suggesting, the same as if you were to manually create a post and let it auto generate the excerpt.
The tag field doesn't work, but tags in taxonomies works just fine. What is the tag field for?
I am not to sure what you mean by the tag field, can you please attach a screenshot this?
I had to change all my categories to numbers to import them, then change them back to text. It wouldn't match the category titles. Is it possible to match the text?
By default it should check category titles, for example if you had a category with the name "Category 1",