Minified SVG is a single unreadable line, which is fine for shipping and miserable for editing. Beautifying restores consistent indentation and line breaks so you can find the element you need, understand the nesting, and get a readable diff when the file is under version control.
No. Whitespace between SVG elements is not rendered, so indentation is purely for human readability.
Minify before shipping if the SVG is inlined in HTML or CSS, where every byte is served on each request. If the file is served separately and gzipped, the difference is much smaller and readability may be worth more.
A minified SVG is one enormous line, so any change shows as the whole file being rewritten. Formatted markup produces diffs you can actually read and review.
Not directly, but badly nested or unclosed tags usually become obvious once the indentation is applied, because the structure stops lining up the way you expect. Use the Code to SVG renderer if you want to confirm the file still draws correctly.