I don't believe adding a blog to a website would generally cause a drop in authority. But here are a few scenarios where I feel it could drop your authority.
- It could be negative if the content added to that blog section is duplicate content.
- It could be negative if the content is too thin in that blog section.
- It could be negative if the bounce back rate is too high in the blog section.
- It could be negative if the blog is overly syndicated to other low quality blogs.
So unless you fall into one of those, then I don't think your drop in authority is likely related to you adding a blog. Now if you lost rank, then perhaps google is trying to determine between pages that are too similar which one should rank.
To your 2nd question, internal links to your homepage will most likely not hurt you especially if they are part of the navigation structure. It is natural for a page to link back to the home page in the navigation. But links to your home page within the blog content that are keyword stuffed could hurt you, these links are not natural.
Have you lost a significant amount of traffic? What exactly do you consider a loss of authority?