How to save the profiles that I find most interesting?

If you find a member particularly interesting, visit their profile and click/tap the Add to Pinned bookmark icon. 

You can find your Pinned profiles by going to "Matches" and then by applying the filter Pinned

To remove a match from your Pinned, simply visit the profile and click/tap the Remove from Pinned bookmark icon.

On the app, add or remove someone from your Pinned by visiting the profile and tapping the star in the top right-hand corner of the profile.