Answer to Question 1: Yes, it is possible that castings and coupons will have different mechanical properties, depending on the cooling rate, which affects final microstructure.
Answer to Question 2: No, hardness is not the only method for determining "strength". In fact, hardness is not specified as a requirement in ASTM A 536-- yield strength, tensile strength, and elongation are the requirements. Hardness is a specified requirement for SAE J434, which is another specification for ductile/nodular iron.
If you have actually specified ASTM A 536 on your Engineering Drawing, then your casting vendor should be providing you will tensile test data, as required by section 4, Tensile Requirements. This testing will be performed on separately cast test specimens only, unless you have also specified that test bars be machined from actual castings. Also, section 6 of ASTM A 536 provides details on how the test specimens should be prepared.
Answer to Question 3: You did not provide enough data for me to be sure. I recommend that you discuss the following with your casting vendor: creating a test matrix that includes all of the pertinent variables related to strength. That is, perform tensile tests on separately cast specimens, as well as on specimens obtained from representative area(s) on the casting. Also perform hardness tests on both of these different types of specimens. The final testing to correlate all of this would be to analyze the microsructure of the separately cast test specimens with that of the actual castings. The goal is to obtain similar microstructure and properties in both the test specimens and the actual castings.
Answer to Question 4: Correlating hardness to tensile strength does differ from material to material, so you should only use data that is appropriate to cast iron. You should definitely NOT use the standard data obtained on steel specimens that appears in ASTM E 140, SAE J417, Machinery's Handbook, etc. There does exist some good data on strength (yield & tensile) vs. hardness and elongation vs. hardness in ASM HANDBOOK Volume 1, Properties and Selection: Irons, Steel, and High-Performance Alloys. The section on ductile iron is approximately 20 pages, and would give you a lot of background on the material, microstructure, properties, etc.
The entire book is somewhat expensive (~ $200 nonmember, $160 member), but it is well worth the price, as is the entire ASM HANDBOOK collection. ASM also sells a volume called ASM SPECIALTY HANDBOOK, Cast Irons, which is 494 pages, and sells for ~ $210 nonmember, $170 member. It contains this info, as well as all of the information on cast iron that is printed in the 21 different volumes of the ASM HANDBOOK series (Vol 15 is Casting, Volume 16 is Machining, Volume 8 is Mechanical Testing, etc.)
A lot of this information is also available in the METALS HANDBOOK, which is a condensed version of the 21 separate volumes of the ASM HANDBOOK series. The price of this book is ~ $210 nonmember, $170 member. If you or your someone that works at your casting vendor is already a member of ASM, the METALS HANDBOOK information is available free over their website:
You can also obtain more information on how to become a memeber, how to purchase books, etc.
If you have any questions, feel free to post another message. Good luck.