Upgrade Issues from 11.5.10 to R12

I would say, the relationship between Payment Method and the Processing Type used in Payment process Profile is not on a ONE TO ONE basis, it is more like Many to One / One to Many relationship Type...ALSO THERE IS NO DEPENDENCY BETWEEN PAYMENT METHOD AND PROCESSING TYPE in PPP

The Processing type in the Payment process profile indicates how the Payment instruction is going to be processed, which is a background process/system configuration and not shared in front end.
The Payment method is an indication as to the available modes of payment shared in the Front end, it does not really have any processing related information ....(apart from seeded/user defined validations)

In Short any thing that is not printed would be electronic, hence Electronic, Wire and Clearing would all fall under Electronic processing Type.

1) Check
2) Electronic
3) Wire
4) Clearing

1) What is the purpose and meaning of the column: 'Processing Type' at the PPP header level?

 Ans) It means how the Payment Instruction would be processed.

2) Does it means that for 'Check' payment method we should choose only and only 'Printed' option and for 'Electronic' payment method we should select only and only 'Electronic' ,does this options is linked to these payment method?

Ans) NEED NOT BE ! I did a test case myself to get clarified, system would allow you to select a payment process profile of electronic type to a CHECK payment method ......It is totally up to the organization to decide how they want to process their payment instruction, there is no dependency on the payment method.... You could process a CHECK Payment electronically, you could process a WIRE payment in printed fashion as well ..

3) We have remaining two payment method: 'Wire' and 'Clearing' for which we need to configure payment process proifle and for these two payment methods we don't have any option as 'Processing Type' as 'Wire' or 'Clearing', so what should be selected as prcossing type for 'Wire' and 'Clearing' payment method.

Ans)Select as Electronic for Wire and Clearing payment methods..

4) We did not see payment method as 'Clearing' in R12 while creating AP invoices, even though this payment method is enabled in Payment Administrator...

Ans) payment method was inactivated with the following explanation: "This is one of the seeded payment methods coming from AP, but it was decided to seed it as inactive so that it will not appear in LOVs automatically in release 12. This payment method is an odd work around to deal with inter-company payments prior to release 12 and its use should be discouraged in the new release." Customers can change the status to ACTIVE if they want to use this Payment Method. Inter-Company Payments
should be done using Oracle Treasury. Refer (ID 864855.1 - Why The Clearing Payment Method Is Inactive In R12?)

Additional point - when you create your payment process profile, there is a section called USAGE RULES, where you have a region for Payment Methods. You have to select the payment methods that can access this payment process profile, by default the value is selected as ALL ... if you do not want it to be available for all,you can select specific payment methods ... that is
1) Payment Process Profile of PRINTED processing Type should be available for CHECK payment method only
2) Payment Process Profile of ELECTRONIC processing Type should be available for WIRE, ELECTRONIC and CLEARING payment method only
This is a configurable control and not a system restriction / intended behaviour.