MRP uses the information in the Planning Data tab of the Inventory Part in its order lot sizing calculations. MRP (except for multi-site planned parts) does not consider anything in the Supplier for Purchase Part record in its order lot sizing calculations.
For all part types (manufactured or purchased), the relevant fields are: Planning Method, Safety Stock, Min/Max/Mult Lot Sizes, and Scrap Factor (%).
Std Lot Size is not used by MRP in any of its calculations. Std Lot Size is used only: 1) for calculating the manufacturing lead time (for that specific lot size) and 2) in Costing Calculation for spreading the Setup Costs over the Standard Lot Size for better unit costing.
Min Order Qty on the Supplier for Purchase Part page only comes into play when a Purchase Requisition is entered manually or converted to a Purchase Order. The user will be presented with an information message that "The minimum quantity when ordering Part No [xxx] from Supplier [yyy] is [z] EA." There is no hard stop here; the Purchase Order can be created under the Min Order Qty. For convenience, though, you could set the Min Order Qty on the Supplier for PP equal to the Inventory Part Min Lot Size to avoid this information message.
@asn I do not understand the statement "Since the inventory part cannot be blank,...". Which field are you referring to?
Supplier Manufacturing Lead Time, along with data in any Supply Chain Matrix, will be used to determine the Latest Order Date on the Purchase Requisition Line.