1957 3-speed overdrive transmission

I am working at restoring a 1957 bird and have a couple of questions.
1. I noticed that first gear does not appear to be synchronized with 2nd or 3rd. Is this correct or is something broken?
2. What are the correct lubricants for this transmission. Are the 3 spd and the overdrive units the same or do they take different lubricants?

3. Clutch pedal seems very far out on engagement. How do you adjust this?

Thanks in advance for your help.
I know on my '55 with overdrive no sync when shifting into 1st gear you must stop. 2nd and third you can shift up and down. All lube should be 75-90w gear lube, the trans (manual of course) does not make a difference. The clutch adj is under the car at the clutch fork end. It has a threaded locking nut you must loosen and turn the clutch rod either in (to give less throw, shorten) or out (giving you more throw, longer). Sounds like you need to shorten the rod (turn it in). The clutch should engage about 2" from the floor as you release. A lot is done by feel as you have many factors with the linkage wear, and clutch wear also. Check all rods (hole ends) for wear also. Hope this helps....
I have a 3 speed and have been told it has Overdrive. i cannot find a selection lever inside but can see what i think is a selection cable coming from what i think is the Overdrive unit. is there somewhere i can see pics of the set up as it should be?
Tezza--I sold the one I restored a couple years ago. However the OD tranny is pretty distinctive. First there should be a lockout cable that allows you to de-select the OD. That is done via an underdash handle that goes to the back of the tranny. Second, those are electric shift OD units. When the cable and underdash handle is pushed fully forward the OD unit can be activated. That is done by accelerating a little until you are over abt 35mph, letting off the gas pedal and you should feel it sort of clunk or engage. The Tach should drop in RPM when you do this. Also, this is a free wheeling transmission so when you let off the gas the car would coast. You can engage the OD unit in all three gears but first is a challenge to get to 35MPH or so. If you floor the gas pedal the pedal should engage a switch under the pedal and kick the transmission out of OD.The overdrive in cars of those years was different that that of today as it was electrically controlled rather than a gearshift position. It did work pretty well. That transmission was also used in many Ford and other brands and I had one in my 1950 Mercury when I was a teenager.

Hope that helps