HELP What Model is this GT? LT? 16GT Twin?...

There has to be some experts here that can tell me what i have. see link for photo:   https://2img.net/r/ihimg/photo/my-images/694/qzhn.jpg    

Two days ago i bought this tractor from a guy whos father-in-law died and left him the tractor. I come to find out that this is a Sears tractor made by Murray. I only know the following:

Sears 502.257040
Mfg date 8223... is that 1978?

Engine Briggs & Stratton
Model Type Code
401707 0130 01 78040512


I've spent a few hours on the internet and think that I have a Sears 16 HP Lawn and Garden Tractor but I don’t know if it is a GT 16 or a LT 16 or a GT16 Twin...? I'm rather confused...

I believe the tractor was painted gray (see photo below) in an attempt to match its original color (whatever it was) decal looks to be original. Can't find any other decals so photos of what it should look like would be appreciated.... also I'm interested in the following:

1) How do you work the electric 3-point hitch...when it goes down shouldn’t it lift rear tires of tractor when rototiller is lowered?
2) Where might I find an owners manual for tractor/engine / electric 3-point?
3) What mower deck(s) fits this tractor and where can I get one (with attaching hardware)?
4) Why is this so slow... is there an overdrive High/Low gear?

Any Help is really appreciated!

My dilemma was solved by the helpful folks at Murray Owners World.... it appears that i have a 1978 Sears GT 16 Twin.