I have the following questions about GCP's free tier:
Would it be possible to host a web application on Compute Engine (backend, frontend and postgresql database) using docker?
Is it possible to use a pipeline in Github Actions for automated deployment?
Is it possible to set up an automated database backup, for example once a week?
I would just like to know if it is possible without implementation details
Yes, it's possible to host all those things in the free tier.
Regarding DB backups, you'd need to write the automation yourself for the 1/week backup of your data if you're planning to host it in Docker which I wouldn't recommend. Otherwise, CloudSQL could do this for you automatically as part of the managed service. The cheapest you can get CloudSQL for would be ~$7.665/month according to the pricing page.
You do also get as part of the free tier an e2-micro instance which you could put your db on if you so choose instead of using the managed CloudSQL service, however then you'd need to manage the automatic upgrades, backups, scripts etc yourself.
If your application code is in a docker container anyway, I'd recommend checking out Cloud Run which pay-per-use with a very generous free tier. Unless you're doing very big numbers, which for a small/personal site would be hard to imagine, then you'll be in the free tier. You can use the native cloud build tool for continuous deployment or you can script it up yourself with github actions.
In summary:
e2-micro instance for your DBHope that helps!