Is there any built-in mechanism to manually edit records posted to information registers? I mean, for example, if I posted any document and want to change a bit the way it was posted, like in the 1c Accounting Russian edition, is there is a simple way to do this or I have to write the whole mechanism by myself?

The posting procedure which is generated by the wizard is a simple 1C:Script which can be edited and you can use any posting mechanism you like there.
To make corrections which you mentioned you need to create a document which makes register records with all the same, but negative sign in amount to null the records you don't like and then to make new records. But use this very carefully due to you will provide a very complicated for users mechanism in your application.