If it will shift when the engine is off, but not while it is running your clutch is not working
If you have bleed the system and If it will not go into gear with the engine running, the clutch pressure plate may have failed.
synchro plates went out
The brake pedal has to be fully depressed for the stick to engage.
get a new engine DUMMY!
If second is the only gear that does not work, there is an internal failure. The transmission will need repaired or replaced.
friction plate stuck to flywheel - In Open space Start car and allow to reach normal running temperature . Turn off engage first gear leave clutch pedal . Keep starting and stopping engine until friction plate releases.. Or maybe completely worn out usual sign is burning smell .
Switch to 4th gear!
if your talking about when your cranking the engine over with the cap off, then you have a broken distributor gear or shaft or bad camshaft gear.
an engine if running usually heats up, are you talking heat in car? need new thermostat
It won't hurt. As long as the engine is running the transmission fluid is being circulated, keeping everything lubricated and the fluid cooled. As to if you will actually get better fuel consumption or not, I can't say. Out of gear the engine will use fuel, and in gear it wont. In gear the engine will slow the car down, and out of gear it won't. Which of the two above will give better mileage?
clutch gone try putting into gear then start engine be ready to shut engine off