It is possible to restore just the database from a Full backup if you do not have a Database Only backup , this can be done using the normal restore tool with a couple of extra steps or in fact if you are comfortable with using a database management tool such as phpMyAdmin or equivalent you can simply extract the database dump from the Full backup and import it (note: using phpMyAdmin or similar only applies if it is a strict restore where no information in the database or in site files is required to change).
It is possible to exclude selected directories (and hence any files and subdirectories contained within) from a backup and also specific files can be excluded (for example, you can exclude one large file in a directory if you do not want to exclude the whole directory).
You can choose to skip the database dump when making a Full backup but generally this is not recommended as generally Full backups are what you take to be able to fully restore your site or fully migrate it to another server - but it can be done. You can also exclude specific tables (for example, an option you can use if you have some enormous statistics table that is not essential to be backed up) and also include specific tables that may not be directly part of your site but may relate to some related funtionality.
Please let us know if this is the information you require or whether you have any additional question or clarification required in this respect, thanks.