If I had a blog using WordPress.com free tier, and then later decide to upgrade it so I can use a custom domain, more customisations, etc. Will this affect any SEO/ranking progress?
If you change your domain name, yes, it will affect your rankings. You need to inform Google of the domain name change via their tool in Google Search Console.
If you change your domain name, yes, it will affect your rankings. You need to inform Google of the domain name change via their tool in Google Search Console.