Right on, write on about whatever you feel best.

At home I'm using HSDPA broadband connection, is it also DHCP?
and what about wireless connection(wi-fi)?

If you get the IP automatically then most probably it will be DHCP.

You can check it using CMD command: netsh interface ip show config
In the results you may get single or multiple interface settings based on your current network config

Go with the interface name that you wish to see the settings,
You will see the below sentence in the results:
DHCP Enabled: YES (If DHCP is enabled)
DHCP Enabled: NO (If DHCP is disabled)

Or you can go to Network Connection and check from there.