is there any problems with runing synthetic motor oil in a 1987 samurai.
Maybe.
Most Samurai's leak. Especially around the distributor. If yours doesn't leak, then there's no problem. The BS about "don't use synthetic, it'll
cause a leak." is just that - BS. There's a few people that claim this is true, but study after study is unable to replicate this. Further, there's no "magic" chemical that eats away sludge and causes leaks - it's just preposterous.
is there any advantages with running synthetic in it? performace, heat, friction?
There's 2 main advantages of synthetic:
1) Because it's starts out with an improved "base" oil, they're able to put in a better detergent package (the chemicals that combat the formulation of sludge, shearing, acid from combustion process etc). This superior detergent package means the oil can stay in the engine longer (10,000 miles +), so you don't have to change the oil as frequently.
2) Some synthetic oils "stick" better when cold, and provide better lubrication during startup. It's unknown how much (if any) this helps engine longevity. Considering engines have lasted 200,000+ miles on conventional oil (my Celica was running strong at 264,000 miles when I sold it, and it never had synthetic in it), I have my doubts as to how much this really helps.
If you have an engine that doesn't leak, or eat oil, and you're interested in going longer between oil changes, synthetic makes sense. It can save you money by lasting 3-5x longer than conventional oil. If you change your oil every 3,000-6,000 miles, or your engine leaks / eats oil, there's no cost benefit to using synthetic. Conventional oil sold in the US is REQUIRED to last a minimum of 6,000 miles.