Can I use my old SSL certificate with websites in subfolders?

Since it's still same domain, do we need to change anything regarding our SSL?

Since the domain is the same and paths are not stored in the certificate, you can continue using your old certificate.

Even if dk and no is folder names in our IIS virtual folder?

The internal configuration does not matter here (the client verifying the certificate does not know anything about it anyway), as long as the web server delivers both sites under the same domain name (which is what you described).

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If you'd use subdomains, things might change (if you haven't got a wildcard certificate, which is not the common case and not best practice). So if you'd be using dk.website.company.com and no.website.company.com, you would either need a wildcard certificate for *.website.company.com or a certificate matching all that domains (also consider www.website.company.com in this case).

You're fine. A TLS certificate validates the server machine (or host machine), not the page or folder.

For example, all of *.stackexchange.com shares a single certificate. By inspecting the cert for this page in Chrome:

Issued to: ssl333133.cloudflaressl.com
Subject Alternative Names: DNS Name=ssl333133.cloudflaressl.com
                           DNS Name=*.stackexchange.com
                           DNS Name=stackexchange.com

If you wanted to add more host machines each with a different domain name, for example:

server1.website.company.com
server2.website.company.com
...

then you might have to look at either getting more certificates, or getting a wildcard cert (*.website.company.com). For your question: yes, you can add as much content as you want to the same host machine without needing to change your certificate.