Haarlem, The Netherlands

Yeps, create an application and a device within that application.
Connect your board via otaa or abp to ttn. You say you’ve got a LoPy coming in, but, if I remember correctly, there are some difficulties connecting it to TTN.

If messages are received by ttn, the will appear in the data-tab. But note that once you close the brwoser screen, the data is gone. TTN is just a pass throught, if you want the data to persist you should build something which does this.
Look at the ‘applications’ section of the docs. TTN makes an MQTT stream available in which every received message is being pushed to every listener.
Look at: https://www.thethingsnetwork.org/docs/current/mqtt/

If you want to check the connectivity of your gateway, look here.