So I'll just address the second part, specifically around the popular reaction to the Vietnam War.

It's not really correct to say that public reaction to the Vietnam War at the beginning of conventional US military involvement in 1965 was "indifference". On the contrary, something like 60% of Americans supported military intervention in Vietnam, with only 24% opposing. However, as the war dragged on with mounting casualties, support for the war slipped. You can see some interesting data collected by Gallup here. A majority of Americans supported military intervention in Vietnam from 1965 until April 1967, and a majority opposed intervention only from August 1968 on. However, that opposition continued to grow, until by the end of conventional US military involvement in the war in 1973 public opinion had flipped, with 60% considering US involvement to have been a mistake and 29% supporting it.

While popular support for US involvement for the war held up for several years overall, this support did not translate into support for Lyndon Johnson's handling of the war. Despite early majority support for LBJ, public opinion was soon almost evenly split between support and disapproval for the president's handling of the war, with approval ratings falling to a minority in 1967 before rebounding the following year.

Part of the reason for the fall in public support over 1967 and 1968 is the mounting casualties suffered by US forces. This RAND Corporation study of the War and its public support shows that the vast majority of US cumulative casualties (which by the numbers seems to mean KIA, MIA and wounded) occurred in 1967 and 1968 (the graph is on page 22).

Louis Harris conduced a series of in-depth studies of public opinion about the war during these years, and the RAND report summarizes some of these findings:

"....casualties, and particularly those killed in action (KIA) troubled(emphasis original) the public more than any other factor about the Vietnam War, even though casualties had not directly affected a large percentage of Americans."

The Harris polls showed that while most respondents felt the impact of the Vietnam War in terms of economic effects (especially inflation), most respondents were concerned over the mounting casualties, even if they did not experience these casualties in their own families or social networks. The RAND study links this concern over casualties shown in the Harris polls to the graphic television coverage of the war.

The study notes that a major issue with the conduct of the Vietnam War by the Johnson administration were both the escalating involvement of US military forces in combat in South Vietnam and the limits that the president placed on the scope of permissible combat, for fear that all-out war in Indochina could lead to Chinese intervention and possible nuclear escalation. So while ground forces in 1965 expanded from defending enclaves, to conducting operations 50 km from such enclaves, to engaging in "search and destroy" missions across South Vietnam, the war was simultaneously considered a limited one (Army Reserves were not called up, for example). As Special Assistant Walt Rostow noted in an interview years later:

"We should not go into the war with a bang and a declaration of war because we didn't know whatever secret agreements might exist between Hanoi and Peking and Hanoi and Moscow. That was certainly paramount in his [President Johnson's] mind in his responsibility as Commander-in-Chief."

While many commentators at the time and since have interpreted this as the Johnson administration hoodwinking the American public, there is strong evidence that the Johnson administration feared American public opinion. Johnson and his administration feared that a more mobilized war setting in the country would threaten Johnson's "Great Society" programs, and strengthen opposition from the political Right - opposition that would demand greater military action. Even within the Johnson administration, officials were skeptical of public support for drawn-out fighting in Indochina: Undersecretary of State George Ball cited the fall of public support for the Korean War as casualties mounted to question any long term popular support for war. While Johnson and his administration did track daily public opinion on the war, they largely ignored Ball's arguments and assumed that US public support would stay steady from 1965 on.

Despite the large US military successes in the field in 1965-1967, no decisive victories were won, and no clear end strategy beyond continued attrition was perceivable. This, with the increasing American casualties, largely wore down American public opinion. But not only public opinion, but opinion within the administration as well, something that was evidenced in the release of the Pentagon Papers as seen in The Post. By 1966 Secretary of Defense Robert McNamara began to argue for limited escalation of the conflict, and by 1967 he wrote:

"I see no reasonable way to bring the war to an end soon...[The enemy] has adopted a strategy of keeping us busy and waiting us out (a strategy of attriting our national will)..."

Other administration officials began to back this view, ie scaling back or limiting military operations in order to limit casualties.

When North Vietnam launched its Tet Offensive in February 1968, the war seemed largely unwinnable to both the American public and the Johnson Administration, ironically despite most Viet Cong and North Vietnamese forces being defeated in their offensives. The US halted bombing of North Vietnam in March 1968, Johnson publicly announced that he would not seek reelection, and US diplomats began preliminary peace negotiations with North Vietnam in Paris (of course the war would continue for the US for another five years). The policy of "Vietnamization", ie replacing US forces with South Vietnamese forces, began to to be implemented in this period as well.

A small post-script about American public opinion: even though American public opinion had largely shifted to oppose involvement in the Vietnam War by the early 1970s, it shouldn't be inferred that this meant popular support for the anti-war movement. President Nixon commissioned a study in 1971 by the Opinion Research Corporation that found that only something like 18-30% of respondents approved of antiwar demonstrations, and something like 60-70% disapproved (take it with a grain of salt, although OCR is a real professional polling organization and not just a Nixon outfit). Gallup found that by 1990, approval/disapproval rates were split, meaning that public disapproval mellowed over time. Cornell University's Roper Center (cited in that link) finds that this is pretty consistent with American perceptions of civil disobedience - disapproval is high at the time, but grows increasingly supportive after the fact.

Sources:

Lydia Saad. "Gallup Vault: Hawks vs. Doves on Vietnam" Gallup.com. May 24, 2016

Frank Newport and Joseph Carroll. "Iraq Versus Vietnam: A Comparison of Public Opinion" Gallup.com. August 24, 2005

Carl Brown. "A Creeping Doubt: Public Support for Vietnam in 1967" Roper Center for Public Opinion Research, Cornell University. Link here

"Going Too Far: The American Public’s Attitudes toward Protest Movements" Roper Center for Public Opinion Research, Cornell University. Link here

Lorell, Mark and Charles Kenney. Casualties, Public Opinion and Presidential Policy During the Vietnam War. The Rand Corporation, March 1985. Link here