Looking for a book that teaches writing skills.

As I became aware of my flaw-riddled writing,
I would like to have a book with writing tips that includes correct use of punctuation, proper structure, decent handwriting, and etc.
A book that is authoritative and concise.

Please recommend one for me.

I don't know of one book that combines all that. Any good grammar book will cover punctuation. My favorite is Dianne Hacker's A Writer's Reference.

There are many more.

If by structure you mean grammar, that will be there, too. If you mean style, find a good style book. An old classic is Strunk and White's The Elements of Style. And you might enjoy Kurt Vonnegut's more recent Pity the Reader.

There are many more.

Handwriting is a completely separate topic. One promising title is Sally Sanders' The Print and Cursive Handwriting Workbook.

There are many more.

Use Google! It will show you many more.