Newly created Posts page not working properly

We purchased a business and with it came this www.remarpro.com website. (www.sailwanaka.co.nz) I’ve inherited some old posts and code that are screwing up a new blog post page I’m trying to create.
Any ideas on how to start anew, and delete the old code that’s showing up? I’m not good at writing html, so please explain an easy fix or tell me I need to get professional help. (Despite what my wife says)
Here’s the link:
https://sailwanaka.co.nz/whats-up-blog
1. When I try to create a new post, it doesn’t show up.
2. This old heading and text, and broken link show up:
“Lake Wanaka Yacht Charters, New Zealand”
Broken image link
“Latest News” hyper link to https://www.sailwanaka.co.nz/category/latest-news which, when clicked shows error 404.
PS: I’ve not yet upgraded to 4.7 because I’ve not yet figured out how to do a backup.
Thanks!
Randall