I am connected to internet, but I can not connect to appstore nor to software update. What should I do to connect o appstore and to make a software update?

See the following Apple articles:

Check the status of your network on Mac

Check the status of your network on Mac - Apple Support

You need to have a good Service and/or Wi-Fi.

If they are On, turn Off Hotspot & VPN.

Charge the battery > 70%.

Turn Off VPN, see -> Change VPN settings on Mac

Change VPN settings on Mac – Apple Support (UK)

Make sure you don't have a firewall enabled: Change Firewall settings on Mac – Apple Support (UK)

If your Mac isn't connecting to the internet over Wi-Fi

If your Mac isn't connecting to the internet over Wi-Fi - Apple Support

If you can't connect to the App Store, iTunes Store, or other Apple services

If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

👉 If you tried all of the above steps and you still can’t connect, contact Apple Support.