1) model: check your frame number starts with three chars (should be 3AJ or 1VJ) this is your model. Same chars and number should be on top right of engine. You could have a different namber, same firs three chars, means that previous owner changed engine with another same model, or sometimes you can have also first three chars different, meaning that engine comes from a different model (basically all 595 are similar, many adaptations possible).
So when you search for spare parts, first thing is your frame three letters, then, if different engine letters for engine parts. See also here: Termine
2)exhaust: rusty exhaust is a standard, downpipes can be replaced with small efforts with YAMAHA TTR\TTE\TTS ones, stainless, 50\70 euro on ebay. Silencer stainless is around 250\300 euro, if your has no holes maybe a hi temp paint and some clean every 6 months could work. (Same thing for downpipes)
3) rust on tank depends where if not visible clean, pass a rust protection paint with a brush
4) use a specific oil for bikes, car oil can contain additives not good for the clutch. Besides this, everyone has his personal recipe for oil.. I use a full sinth, 10-50 w change with filter every 5000 km