"...what gun shot that round marked "121..." Might be a 155 howitzer or an 8" arty projectile. Hard to tell from the picture. Your whole head will fit in the breech of an M109's 155mm gun. An M109 isn't a tank though. SP Arty.
"...Were they better in the mud/sand/snow than regular Deuce & a halfs?..." Yep. Wheels don't do well in mud, sand and snow. Half-tracks had light armour too. Mechanised infantry vehicles and wheeled arty tow vehicles.
"...early Sherman tanks were no match for Tigers and Panzers..." 'Panzer' is the German word for 'tank'. No Sherman was a match for a Tiger or Panther. The M4 tank was obsolete, by 1944. Armour was too thin. Even a Firefly(Sherman with a 90mm gun. Not used by the U.S.) would get swatted by a Tiger or Panther, if the Firefly didn't shoot first. They were even with Mk III and Mk IV Panzers. They weren't called Tommy Cookers and Ronsons for nothing. Fortunately, there weren't many Tigers or Panthers and neither were unreliable.
Stupid thing is that there was a better tank ready to be made that would have been able to tangle with a Tiger, but Patton said it wasn't needed. He thought tanks were for getting into the enemy rear and blowing stuff up, not for fighting enemy tanks. A lot of armoured troppies died because of him.
If any of ya'll ever get to the Toronto area, the CFB Borden Armoured Museum is worth the 45 minute or so drive. Nobody ever says, "Don't climb on the tanks." German, Allied (both wars) and post war plus assorted crew served MG's and arty, outside, you can pet. The Small Arms Museum is open Sunday afternoon, is free and has one of the German 'shoot around corners' rifles, et al. Aircraft as well. There's a CF5A you can pet. Can't climb on it though.