That serial number says its a 356 series, unfortunatly i do not have that literature on that series so i cannot with any certainty tell you what pressures to check for.

the sloppy linkage can cause a starting problem because it may not be letting it return to "true" neutral, the neutral start switch if not centered will not allow the truck to start. This is why your having to move the lever around to get it to start.
The brake valve on the side of the transmission is the inching valve, this disengages the clutches when the brake pedal is depressed.
The sloppy linkage MAY be causing your slow engaging problem if the spool is not moving completely in place to change the flow at first, it may be on the verge of being engaged and as the engine is running vibration may be allowing it move farther after a bit.
Your steering issue i'm not sure about, there are a couple things that can cause steering problems, one is low engine idle rpm's, if too low can cause a low pressure scenario which may not be enough to allow for hydraulic and steering simultaneously. Most trucks have a steering priority valve that works inline with the hydraulic system and allows some pressure to be prioritized to steering full time. Low rpm's or low pressure may cause the valve not to shift properly and it could be effecting the steering.
One other cause would be a bad or low pressure situation on the steering orbital valve on the steering wheel column, i would check that pressure and also check the pressure relief valve for a broken spring. Check the oil supply and make sure it is getting fluid, there will be a pressure line connecting that you can put a pressure guage on, may be able to tap the hydraulic control valve at the steering pressure port which is usually located on the main hydraulic control valve auxillary side.