Is it possible to backup and restore InnoDB tables on Oracle's MySQL 5.7.19 Server with Percona Xtrabackup?
After doing some research and re-reading the manuals I found the next:


I had done so called partial backups, that mean that the restore process is a little bit different - you need to specify --export option when doing the restore process (see Restoring Individual Tables)


If you are on Percona Server you can try to use innodb_expand_import option and avoid of some routine operations.
If you are on MySQL server - you must also to do the schema dumps. Then do the tricks with ALTER TABLE xxx DISCARD TABLESPACE and ALTER TABLE xxx IMPORT TABLESPACE for an every single table. (See here)

I did the restore without specifying the --export, so had the problems with those .frm's.
If you have stored procedures/etc - maybe you need to backup them as well. I have no chance to check that.