This question raises interesting questions. However, there are some confusions in the question. And I respectfully disagree with some of the factual and opinion content of the answers previously posted.
Nearly all factual aspects of the conflict between the Tutsi and Hutu during the post-independence period are contested. This is regrettable since much of the factual material has become settled by historical research and some of the judgements of the International Criminal Tribunal for Rwanda. It is important to be cautious about accepting many views on the facts, since many people have hidden agendas and axes to grind. My answers below are based, with the exception of that in respect of the Congo, on the facts set out by the much respected, late Dr. Alison des Forges of Human Rights Watch, who appeared as an expert witness in nearly all ICTR cases. Her various testimonies are available online, as is her 800 plus page account: “Leave None to Tell the Story”.
First, some brief background is necessary to make sense of the questions and responses.
By the late 1980s, the Rwandan diaspora was estimated to number about 600,000 people. Most of them lived in countries next to Rwanda. In Uganda, Rwandan refugees created the RPF in early 1988. The RPF was prepared to use force to enforce the return of refugees. It was dominated by second generation refugee Tutsis, many of whom had developed sophisticated military skills in the Ugandan National Resistance Army. The RPF rejected the ethnic divisions reinforced by the ex-colonial masters. Paul Kagame had been deputy head of military intelligence for the NRA, and he assumed command of the Rwandan Patriotic Army (RPA) , the fighting arm of the RPF. The RPF also recruited Hutus and appointed a Hutu as president of the RPF. On February 8, 1993, when the government was avoiding negotiations, the RPF broke a 1992 ceasefire and launched an attack along the northern front and pushed the government army back. With the assistance of French troops, the RPF advance was halted. The RPF agreed to withdraw to its original position.
Negotiations resumed. This time the French indicated that, unless, the government negotiated in good faith, they would not continue to fight the government’s battles, and the donor community threatened to withdraw financial support. On August 4, 1993, the government and the RPF signed a final agreement. A power-sharing transitional government was to be formed in which the government’s Hutu supporters were to lose considerable power. A new Rwandan army was to be made up of 60% government and 40% RPF personnel. An RPF force was allowed to enter the capital to protect their leaders in the proposed new government. When this happened, some Tutsis were emboldened to come out in open sympathy for the RPF and some went for training to the RPF base at Mulindi, in northern Rwanda. Many Hutus in the army and Hutus in the political arena were actively hostile to the agreement. Then, in November 1993, President Habyarimana denounced the accords as “nothing but a scrap of paper.” Dr. des Forges states that genocide planning by a small group of Hutu extremists started over a year before it began.
From January 1993, when planning for Hutu civilian self-defence began, through March 1994, Dr. des Forges states that “Rwanda imported more than half a million machetes, enough for every third Hutu adult male. This was about double the number imported in previous years.” According to the only local manufacturer of machetes, the company sold an unusually high number of the machetes in the second half of 1993 to two employees connected with extremist Hutu parties. During 1993, the government military distributed firearms to militias and the civilian self-defense programmes that it had initiated. After October 1993, distribution of firearms, grenades, and machetes increased.
I understand the questions to be:
(a) “ … with Tutsis being a minority and 70% of this minority exterminated, how they could win the civil war and secure the power?”
So the answer to (a) is that the fighting by the RPF was carried on by soldiers from the diaspora with some recruits from inside Rwanda. The massacre of the civilian population inside Rwanda did not – simply in terms of numbers – affect the capacity of the RPF to fight.
(b) “How this new government could be successful to secure loyalty of the army so to defeat Congo in the aftermath?”
The answer to (b), if I understand it correctly, is that the new RPF government, after July 1994, created a new army based on its core invading force together with new recruits. The RPF had always made a special point of recruiting whenever it could from the Hutu community as well as the Tutsi community, since it had an ideology of rejection of ethnicity. [That does not mean that ethnic Tutsis did not dominate within their ranks. It did.] In the Congo, the situation was complicated by expatriate Rwandans from both communities, and the Hutu refugees and their armed forces who were the specific target of the government effort. The Rwandan government forces received significant assistance from sympathisers in the Congolese community of a semi-Tutsi background. [It is a complicated story and it would take a considerable amount of space to set out the full story.]
(c) “Why the Hutus who were the majority in the country fled it in the aftermath of the Tutsi takeover?”
The answer to (c) is that the Hutu expected to be targeted by the RPF after their victory. Additionally, the French Operation Turquoise enabled a safe zone to be created that allowed a corridor for evacuation – this was used not only by genocidaires to escape, but also Hutu civilians who expected massacres by the RPF invaders. These massacres did occur, and this accelerated the exodus.
(d) “It seems that the Hutu government was defeated in immediate consequence of the genocide. How killing the Tutsi could harm the Hutu effort to win the civil war?”
The answer to (d) is that the genocide was motivated by its perpetrators as targeting supporters of the invading RPF. And Dr. des Forges testified that “By early April, the RPF had some 600 cells throughout the country, 147 of them in Kigali. With each group counting between six and twelve members, this made a total of between 3,600 and 7,200 persons… The greatest number, some 700 to 1,400, were in the capital but few of them had firearms.” But the genocide was directed at all Tutsis and moderate Hutus, not a minute proportion of the population who supported the RPF. Did the genocide have a negative impact on the capacity of the government forces to fight the RPF? This is a matter of opinion and a judgement call. On balance, I do not think so, but on this, reasonable people can differ. First, the killing of moderate Hutu opponents of extremist Hutu power, and the Belgian UN peacekeepers in the first stages of the genocide probably removed any chance of international intervention that might have delayed the RPF victory. Second, the diversion of resources from the battlefield was not a key feature of the genocide. Most of the killers were Hutu militia, civil-defence personnel, communal policemen, and male civilians. Killings attributable just to the conventional military after the initial bloodletting by the army [especially the Presidential guard] were not a principal feature of the genocide. The RPF victory was reasonably quick, and it is unlikely that the killing by the militia, police, and civilian elements had a significant impact on the outcome. The RPF was by far the superior force in terms of tactics, strategy, leadership and morale by late 1993, and that is the most significant factor in the victory. UN Force commander, Romeo Dallaire, deals with the relative merits of the forces in his work: "Shake Hands with the Devil".
You are referred to the work and testimonies of Alison des Forges, Linda Melvern, Philip Reyntjens, Andre Gichoua, Romeo Dallaire and Francois-Xavier Nsanzuwera.