Can i use synthetic blend motor oil 5w 20 high mileage in my 2009 mazda rx 8?

No. Either go conventional oil or go Full Synthetic like Mobil 1, Royal Purple, etc. Also, 5w-20 is too thin for a wankel. 5w-30 is the thinnest I'd use in ANYTHING.

Sure you can, you can use water if you want to. Should you is a lot better question.

If your vehicle recommends 5w 20w motor oil high mileage oil is great to use. I prefer Valvoline High mileage blend.

No. Absolutely not. 

Rotary engines MUST ONLY use mineral oils. Any synthetic oil can cause serious internal damage requiring an engine rebuild.

Rotaries lubricate the rotor “piston” and the plenum chamber in a similar way to 2-stroke engines: they inject a tiny bit of mineral oil into the plenum chamber and it after lubricating the rotor tip seals and other parts it gets burnt completely and the residue (smoke) leaves with the exhaust.

Synthetic oils and synthetic blends have far higher resistance to being burnt. So instead they form varnishes inside the plenum chamber and gum things up, particularly the rotor tip seals which must be free to move a little.

That is why all rotary engines have a slightly smoky start up, and although the smoke should be invisible on a warmed-up rotary it’s still there as an air pollutant. That is what killed further use of rotary engines to power cars.

As a rotary owner you have to accept that the engine is just as much as consumable item as the clutch or brakes. So every 80k to around 140k miles the engine needs to come out for an overhaul. Some careful owners who have owned their RX from new get higher mileages between rebuilds.

The 80k rebuilds will often be on cars which were only used for short trips where the engine didn’t often reach full working temperature (but that happens faster on rotaries as they have far less mass than equivalent power piston engines). Also many owners are unaware that before turning the engine off rotaries should be allowed to idle for a minute or so. Sub-80k rebuilds are also typical if anyone has used synthetic or semi-synth oil (running on synthetic can result in rebuilds in as little as 10k miles or fewer).

But even with the right oil and correct engine operation unique to rotaries they don’t often last much more than 140k.

The good news is that they’re smaller and lighter than piston engines and so are much easier to remove than most piston lumps. Mazda also recognised that feature of rotaries so designed those cars to make engine swaps pretty easy. Because rotaries have far fewer moving parts than piston engines they are also faster and cheaper to rebuild: experienced owners with a good workbench and experience of car repairs can often do the job themselves over a weekend by using a rebuild kit, but there are rotary specialist workshops who will deliver a freshly rebuilt engine on an exchange basis. 

Plenty of owners even obtain a spare salvaged engine and then get it rebuilt and put straight into long-term storage after using special oils designed exactly for that job. They then have a spare ready and waiting when required.

I suggest that you join some of the many online forums devoted entirely to Mazda RX owners but also to Wankel engines in general. Mazda were the last to use them but they were certainly not the first.

Read the owner's manual and put the recommended oil.  Not rocket science.