IPhone – Is it possible for the husband to receive message on his phone that have been sent to me.

You could try to recover information from the sqlite file using for example a hex editor. Here is a quote from SQLite FAQ:

I accidentally deleted some important information from my SQLite database. How can I recover it?

If you have a backup copy of your database file, recover the information from your backup. If you do not have a backup, recovery is very difficult. You might be able to find partial string data in a binary dump of the raw database file. Recovering numeric data might also be possible given special tools, though to our knowledge no such tools exist. SQLite is sometimes compiled with the SQLITE_SECURE_DELETE option which overwrites all deleted content with zeros. If that is the case then recovery is clearly impossible. Recovery is also impossible if you have run VACUUM since the data was deleted. If SQLITE_SECURE_DELETE is not used and VACUUM has not been run, then some of the deleted content might still be in the database file, in areas marked for reuse. But, again, there exist no procedures or tools that we know of to help you recover that data.

Hope this helps.

By default apps are copied to iTunes from the phone when syncing. By default apps are copied from iTunes to the phone when syncing. This can be annoying - personally it's my kids who put a thousand irritating games on their phone, but I can see that a husband would be just as bad.

Connect your phones to iTunes. Find them in the left-side menu, or drop-down.

Under the Apps menu you can turn off syncing.