I've noticed heads of state that are monarchs were often (and infact still are) photographed wearing their medals at larger, state affairs. I cant recall ever seeing a US president wear any - but I don't think any president during my lifetime (born early 80s) was in the forces.
Partial answer to your first question:
George Washington had a military career as a militia Lieutenant, and later as General of the Continental Army, before he won the position of first President of the United States.
Other Presidents who served at the level of General commanding an entire army are Dwight Eisenhower and Ulysses Grant. These three are the higest-ranked military leaders to later become President.
Perusing lists of Presidents by military service, I see a pattern: a wave of Presidents who served in a particular war, then a lull, then another wave of Presidents who served in a later war. Ranks of service, and experience in battle, vary widely.
A large number of presidents during the 1800s served in a military unit during one of these wars: the Revolutionary War, the War of 1812, the Creek War, the Seminole War, the American Civil War. The rank achieved, the type of service, and the amount of action seen varies widely.
After 1900, we have Theodore Roosevelt (veteran of the Spanish-American War), Harry Truman (veteran of World War I), bracketing a large number of Presidents who never saw military service.
Afer President Truman, there is a long list of men who served in World War II. Presidents Eisenhower, Kennedy, Johnson, Nixon, Ford, Reagan, and George H.W. Bush all served in that war. Some saw action, some did not.
Finally, there is President George W. Bush, who served in an Air National Guard unit between 1968 and 1972. (His Presidency is inside the 20-year rule, but his service in the National Guard is outside the 20-year rule.)
Thus, if you were born in the early 80s, you have seen three Presidents who had previously served in the military. Only one of those three saw action during a war: George H.W. Bush piloted Navy aircraft during battles in the Pacific Theater of World War II.