Small amount of wordpress post configuration needed

I have a small amount of configuration needed on my website site, within the POSTS template.

I would prefer these changes are hard coded as opposed to being done by installing a plugin.

The changes required include:

1) Remove "POSTED ON [date] BY [author name] from the POST page, and the ARCHIVE page.

2) Instead of displaying the full text, I would like to display CUSTOM post summaries for each post on the category page.

3) Remove the DATE on each post (so that a date doesn't appear on the category/archive page OR the post.

4) Remove the post 'category' link, from the top of each post

5) Reduce the size of the cover photo (featured image) which appears on the category AND on the post page itself.

6) I have a dropdown menu on the right hand sidebar. I would like this open (so that all parent and child categories can be seen).