The British troops were led to the battle of the Long Island by General William Howe.
This is the famous Massachusetts 54th Infantry Regiment, colored troops. They were led by white officers, Colonel Robert Shaw commanding
Grant led the Union troops. Pemberton led the Confederates.
Rommel commanded the Axis troops.
American troops weren't involved in the Battle of El Alamein. The British troops were commanded by Bernard Montgomery.
Gen Santa Ana
The British troops at El Alamein were commanded by Bernard Montgomery. To the best of my knowledge, there were no American troops in that particular battle.
The British general that was leading troops during the Battle of Kaskaskia was William Howe. The British troops surrendered to General George Rogers Clark who led the American troops in this battle.
Battle of Saratoga