Well first congrats on your purchase. As for answers for your questions, yes you just manually shift it without the need of a clutch, it is an automatic clutch, the part on the right handle is the throttle and the lever that was on the left would have been for the rear brake, there is also a foot pedal for the rear brake on the right, the large lever on the top right side of the motor is a decompression valve, you just pull that up when you go to pull start it and it will make it tons easier to pull. The oil dipstick is screwed in on the right, you check the oil by unscrewing it and just resting it in there, and then pull it and check. Depending on whether it is the shifter splines itself are bad or the spines on the shaft coming out of the motor, if its the shifter just get a new one, if its the spline than thats more work, some ppl just solve it by welding but that is slightly frowned upon. Hope I answered all of your questions. Have fun.
1971 ATC90
1984 200s
1983 Autox
1985 200x
198? Yamaha 125
(2) 1985 250sx's
1974 Trail 70
1991 Honda Cub90
1974 Yamaha 125 Dirtbike
1972 Kawasaki 175 Dirtbike
(2) 1980 Chrysler Sno-Runner
(7) 85-87 Toyota Mr2s
(2) 1985 Dodge Ramchargers
1968 Mustang
1972 Beetle
2004 Dodge Ram 1500 HEMI