Split data across databases/machines
What you describe sounds much like horizontal sharding of sorts. That, of course, can be done. To answer your second question, you determine the performance (time/space) impact of your design by building a prototype system and measuring what's important to you.

However, security by obscurity, which seems to be your ultimate goal, is rarely worth the effort.

There are better ways to protect sensitive data, which include encryption (e.g. storage level or transparent database encryption, which obviously should include encrypting backups); row- and column-level access control at the database level; thorough security policies; audit, including possibly wire-level analysis of database traffic; network hardening and intrusion detection; etc. All these methods work well only in combination; looking only at one aspect of your security landscape is counterproductive.