Is it necessary to fix all 404 errors and set up redirects for all broken links?
Google Search Console Help has some solid advice on how best to manage 404 errors under the troubleshooting topic on this page.
The following statement from Google about 404s is particularly interesting
Many (most?) 404 errors are not worth fixing because 404s don't harm your site's indexing or ranking.
But don't confuse this to mean you should not bother to fix any 404 errors.
So, while it is important to fix broken links that show up as errors in Google Search Console, 404 pages that are excluded do not need to be fixed.
A 404 is actually the appropriate thing to show if a page no longer exists
If it is a deleted page that has no replacement or equivalent, returning a 404 is the right thing to do. The report should stop showing the 404 after about a month.
Lastly, a bit of reassurance about being ok with 404s in your reports
If it is a bad URL generated by a script, or that never have existed on your site, you probably don't need to worry about it. It might bother you to see it on your report, but you don't need to fix it, unless the URL is a commonly misspelled link (see below). 404 errors should be dropped from the report after about a month.
For more info and guidelines from Google on how to handle 404s, check out their support site: https://support.google.com/webmasters/answer/7440203?hl=en
If you need help fixing your 404 errors on Shopify, check our Shopify app, Redirectify.