Jaisree,
I think the explanations for the second and third options are extremely clear, I don't think I could explain them any better.
Time series in this context is a standard Product Availability Check concept.
Pegging; including Fixed Pegging, is a Planning concept.
Both of these concepts are similar. For both of these, SAP software creates relationships between supply and demand in Livecache.
ATP time series are created dynamically, similar to Dynamic pegging. Within ATP, using time series, there is generally no way to assign a particular supply element to a particular demand element. The system calculates availability information using Time Series data during ATP, and uses that information to create confirmation results to return back to the calling document (e.g.a sales order). Some exceptions to the above general statement exist.
In Planning, the solution sometimes calls for 'hard-assigning' certain supply elements to certain demand elements. SAP offers several ways to do this, under the umbrella of 'Fixed Pegging'.
Normally, Product availability check is unrelated to Planning, and any Fixed Pegging you may have established for your planning solution is IGNORED during Availability checking. However, if are planning in APO, and if you are using Fixed Pegging (neither of which is required for GATP) in your planning solution, you may elect to have the PAC consider the planning results, vs the more common ATP time series.
If the above is unclear, then I suggest you do not attempt to use option 2 or 3, without first becoming extremely familiar with how fixed pegging interacts with PAC. You can learn more about these topics by creating scenarios in a sandbox and experimenting.
Best Regards,
DB49