Yes, you can use PHPMyAdmin for every database you create. You can also install your own application on your free hosting account (Like Adminer) if you want a different interface.
No need to close topics abruptly unless there is a reason such as going off topic or attacking other users. At the bottom of every topic, you will see a timer which will say that the topic will close after a certain amount of days after the last reply. Because someone may post something relevant or you may have another question.
Last time I checked, running your own phpMyAdmin installation doesn’t work because phpMyAdmin needs to be able to SHOW DATABASES which is not possible on our hosting. Adminer doesn’t need this, and is also much easier to setup, so that would be my recommendation if you don’t want to use our phpMyAdmin installation.
Then there is the fact that, looking at the access logs of basically any site, phpMyAdmin is a beloved target for hackers to try and get into your database. So if you are going to use phpMyAdmin, I strongly suggest to also protect the phpMyAdmin installation with a Password Protected Directory or an IP address whitelist so hackers won’t even be able to try to guess your credentials.