All the banks in the Greek part of Cyprus have a SWIFT code and don't require any intermediary to send/receive funds they have as well IBAN account numbers.
Yes, as discussed a few times here on the forum, most banks in Cyprus offer Internet banking in English from where you can manage your daily banking including sending of International Wire Transfers.
Can I have a debit card for let's say hellenic or laiki bank? I read about the banks that they are good, where can I find the service fees of these banks?
Yes these banks like almost most banks in Cyprus offer a Visa Debit Card which can be used in any ATM worldwide! You may consult there website's otherwise let me know.
I think they do.. Because there are large number of investers who recieve payments or funds from foreign countries so thay must be having swift number i think
Nothing is free my friend 🙂 it is not more complicated to open a Cyprus bank account than any other account. You will need to have all DD / KC documents available of course and you need a CV and business description.