Is it possible to create slug on homepage and how?

What you are asking would make those pages NOT be the home page, at least in WordPress’s definition of the homepage.

If you want people to go straight to /some-page and not be able to access the root, then you would create a 301 redirect for this (but there will still technically be something on the root of the domain).

301 redirect example to redirect homepage to some page (this line would go in your .htacess file):

RewriteRule ^$ /some-page [L,R=301]

But, and answering your second question, this will not help SEO and I don’t see why you would want to do this.

If you need to optimise for a particular phrase, then have a page for it and yes put the phrase in the slug of the page. But your home page is your home page. Refer to here for a better explanation of SEO related questions – webmasters.stackexchange.com.

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