Q: How can i get an older version on ios6

Click here for information. If it's not applicable to that application and you didn't keep a copy of the older version, no.

(114299)

The first set of instructions can be performed from a different Apple ID.

If you kept a copy of it, it doesn't matter which Apple ID it's associated with, unless syncing it to the device would cause it to contain protected content from six or more Apple IDs; if that is the case, iTunes won't allow it.

(114300)

Just purchase the app on a computer with the new ID. Then when signed into iCloud and iTunes with the new ID go to Purchased and redownload. However, note the 90 day time period.

iTunes Store: Associating a device or computer to your Apple ID