Wordpress site speed up, mobile version completion

General information for the website: Mediation services
Kind of development: Customization of existing website
Description of requirements/features: 1. Need to complete mobile version of the site, similar to actual desktop version
2. Rectify in total 50 404’s and 301’s as some URLS are not built in wordpress / coding issues, there are still a lot of internal hyper-links that point to the old URL's, even when you re direct them to a new URL.
3. Add breadcrumbs facility to all pages in the CMS as currently able to on some pages, some not.
4. Take a back up of the site , update all plug ins, themes.
5. Remove all plug ins which are not necessary and are slowing down the site.
6. Speed up the site, implement all the following recommendations https://website.grader.com/results/www.effectivedisputesolutions.co.uk
Fix all issues highlighted in Google webmaster tools with regards to the speed of the mobile and desktop versions of the site.
7. Add security to the cms to prevent hacking.
Extra notes: