Hello! Is it allowed to create a new table using \IPS\Db::i()->createTable() when installing a plugin and remove it using \IPS\Db::i()->removeTable() when uninstalling? I need only several fields and I do not want to switch to application just because of it.

Of course it is. Only a note: the right is dropTable.

I would strongly advise to use an application once you have to deal with database tables.

1. It's much easier to maintain the schema via the Application Dev Center, you'll literally only have to set up the fields and the framework will take care of everything else for you. There's no need to create manually any Install, upgrade and uninstall code, like for plugins.
2. Our support tools will try to fix only applications database tables and ignore any broken plugin database tables.