Ok, Let's start from the beginning and deal with the first question.
You have created an MDC database in your trial account providing a password for your SYSTEM user.
For now, to eliminate other possible issues, connect to HCP account using your internet connection (rather than trying to do this from your office for which you need to give a proxy).
Login to your MDC "SAP HANA Cockpit" with your SYSTEM user. You will get a message "You are not authorized to open the SAP HANA Cockpit."
Click on the "OK" button. Your SYSTEM user will be automatically assigned roles 'sap.hana.admin.roles::Administrator'.
Once you are in the cockpit, click on "Manage roles & users" tile. Select your SYSTEM user and provide additional roles. I usually assign all the available roles under "sap.hana.ide....." to the SYSTEM user.
Now try to launch "HANA Web-based Development Workbench". You should be able to access the Editor as SYSTEM user.
Once you are able to get this far, try to connect to MDC database using SYSTEM user from HANA Studio.