If you write this same question on Google You will get a long list of tools, applications and browser addons for running a spelling and grammar check and a link test for websites.

Personal what I do is copy the content of web page and paste it in a Word Processor like MS Word or Libre Office Word and run the spelling and grammar check in it for find the issues. For Final verification I go through the content to make sure it is correct. 

Sometimes the spelling and grammar are correct but the sentence is wrong or is unfit. For this part I don't rely on tools but my knowledge of English.

For link testing there are countless tools of which I prefer the following,

[LinkChecker][1]

[W3C Link Validator][2]


  [1]: https://wummel.github.io/linkchecker/
  [2]: https://validator.w3.org/checklink