The slow start after it sits a while over overnight indicates a leaky check valve in the fuel pressure regulator or fuel pump. Replacing the fuel pump/fuel pressure regulator will fix that... which requires you drop the gas tank. When either of those to check valves leak, it lets gas that is supposed to stay up next to the fuel injectors for fast starting to instead drain back down to the fuel tank.
Your transmission may be in need of an overhaul, but you can try changing its gear lube since there is no telling if the right stuff is in there. Two gear lubes that are approved by Aisin who made your AX-15 include a synthetic 10W-30 engine oil, or Redline MT-90 which can be purchased for less from Summit Racing
If it grinds shifting into Reverse, understand that Reverse gear is not synchronized. To stop Reverse gear from grinding, simply first momentarily shift into a forward gear like 1st gear, THEN shift into Reverse. That momentary shift into a forward gear first will temporarily synchronize Reverse gear which if done correctly, will stop Reverse from grinding.