Two WP installations and SEO
 

I am helping a friend with his website ( local Gym). At the moment, the theme used is nice but missing many features for SEO.

There is a blog section and I am helping him to do SEO and have high-quality articles. But after wasting time with the current theme, I was thinking of installing a separate WP just for the BLOG section so I can use them that will ensure SEO functionality.

I think this is just fine, but I've never done anything like this

What do you think about this?

I wouldn't bother with this, it is overcomplicating things.

I think you are putting too much emphasis on On-Site SEO, when other promotion types will be more important for this type of site, e.g. getting it properly on Google Maps, offline flyer marketing where url is given.