for my bachelor thesis I want to research the LoRaWAN coverage of my city. Is it possible that my node (a field test device) sends its packets only to my gateway. It would not make sense if the node sends its packets to another gateway and thus falsifies the results. Thanks in advance.
Nothing connects to a gateway, the gateway listens for appropriately formatted radio signals and passes on what it hears.
If you have your own private instance of TTS that is not connected to the packet forwarder that will mean only your device’s uplinks will be processed by the network server - I think they are €200 a month.
No, that is not an option. However if your gateway is not part of TTN and your device is not registered in TTN the transmission will be ignored by TTN (after the TTN gateways forwarded the data to the back-end). You can create your own private LoRaWAN instance and connect your gateway to that. For a private instance you can either install The Things Stack on your own hardware/VM, rent an instance from TTI or set up Chirpstack. The last two options are not supported on this forum. The first option requires you to be familiar with Linux and Docker.
Alternatively you could do something many of the students before you have failed to do, which is learn LoRaWAN well enough to know that the uplink messages include all the information you need for your project, even if 20 gateways hear your device.
If you can tell us how you are going to collect the messages and show me which part of the uplink message you will use to gather the information you need, you will most likely inspire people to help give you direction when you get stuck. As this is a student project we aren’t going to hand the answers to you on a plate, mostly because your requirements are very academic - we like our devices to be heard by many gateways.
The extensive documentation would be a good starting point.