If you backed your own car into your other car and both suffered damage how will your deductibles and fault be applied and will this likely increase your rate on one car?

Normally both these vehicles would be on the same inscuance policy. If this is the case, usually the Insurance Company will only have one deductible. With any accident there is a chance that there can be an increase. This would be considered At Fault.

It is also possible that your policy has a clause which EXCLUDES a collision between two vehicles on the same policy.

The person who was driving will be considered at fault for the damage to both vehicles. The collision deductible on the car that was moving would apply to the damage on that vehicle and there would not be a deductible for the damage to the parked vehicle. Rate increases will depend on many variables and will be determined by your individual insurance company's policy.