I'll answer the bits of your question I understand, but I don't understand the bit about changing to synthetic oil because your engine leaks. It would leak either kind of oil.
As for whether you need or want to use synthetic, there are two criteria...which are just that: need and want.
Need: do you live somewhere with extreme climate, cold or hot? When I say cold, I mean consistently below zeroF for weeks in the winter. When I say hot, I mean...well, fact is, there is NOWHERE on earth so extremely hot as to matter in such a modern car...so I will modify the criteria: do you have a compromised coolant system? Synthetic oil performs exceptionally in these extremes (excellent flow at extreme cold temps, good protection even at high heat), and provides little noticeable difference in more temperate climes.
Want: primarily due to the excellent low temp flow characteristics, it is likely that synthetic oil will protect your engine at cold startup slightly better, even if "cold" is 90F (remember that operation temp for your engine is around 250F). Thus, if you plan on driving your car until it won't go, you probably would "want" to use synthetic.
As for getting better MPG, if you do a lot of city driving, especially if you don't get your engine up to operating temp, then, yes, synthetic will almost certainly provide some improvement. OTOH, if you mostly drive highway miles, the savings will be negligible.
One thing to never believe is that you can extend you oil changes using synthetic oil. In terms of pure lubricative capacity, even conventional oil will continue to lubricate for thousands and thousands of miles beyond whatever your recommended oil change interval is. The problem is in the chemical additive package, much of which is designed to deplete over time, some of which is designed to "sacrifice" itself to protect your engine (example: "anti-oxidants" in the motor oil will oxidize with volatile chemicals so that those volatiles won't oxidize the metal of the engine). Dispersants help carry non-volatile contaminants in the oil, but have a limited capacity. The point being: change your oil per your manufacturer's recommendations. Not 3000 miles (per anachronistic 1960s misinformation), and not 25000 miles (per Amsoil and their ilk).