No, not everyone would develop Minamata disease.

While Minamata disease occurred among people who had eaten, over a long period of time, large quantities of fish with considerable accumulation of methylmercury, the appearance and severity of their symptoms varied depending on the degree of contamination and the amount of the fish consumed, as well as on the individual's sensitivity to mercury.
It might be added that methylmercury does exist in the natural environment but only at extremely low levels and, given that there is currently no presence of fish contaminated with large quantities of methylmercury, there are no concerns about developing Minamata disease from eating fish.

Because methylmercury in their mother's body was passed on to them.

Minamata disease is caused by methylmercury taken into the body. In some cases, pregnant mothers ate fish contaminated with methylmercury, which crossed the placenta to penetrate into their baby, causing the baby to develop Minamata disease.
This is called fetal Minamata disease.
Some children developed Minamata disease as a result of eating a lot of methylmercury-contaminated fish, in which case it is called infantile Minamata disease.

Severe symptoms may lead to death, but not everyone afflicted with Minamata disease would die of it.

As with any illness, symptoms of Minamata disease vary from case to case, ranging from mild to severe.
Back when Minamata disease was officially found, there were cases in which patients showing extremely severe and fierce symptoms died within a few weeks. Such cases are indicated as "acute."

As of the end of October 2021, there are 397 recognized Minamata disease patients who are alive.

It is never infectious.

Initially, around the time Minamata disease was officially found, an "infectious disease theory" spread while its cause was still not at all clear.
As this wrong information about the disease being "infectious" was passed around, it provided fodder for hurtful discrimination that the patients then became subjected to.
The truth is that Minamata disease is a condition triggered by methylmercury entering the body and is therefore by no means infectious.

It depends on the degree of methylmercury poisoning.

Once damaged, nerve cells never regenerate. It is therefore not possible to get back nerve cells that have been lost as a result of methylmercury poisoning.
Some symptoms can, however, be expected to be reduced to a certain extent through rehabilitation and drug therapies designed to induce a compensatory function using surviving healthy nerve cells.

The answer is no, at least in Japan.

Production of acetaldehyde in the Minamata factory of Shin-Nippon Chisso Hiryo K.K., the source of the methylmercury discharge that caused Minamata disease, was discontinued in 1968. Correspondingly, methylmercury levels in fish from Minamata Bay dropped by degrees.
Nowadays, fish with mercury content exceeding the provisional criteria set by the national government (0.4 ppm for mercury and 0.3 ppm for methylmercury in total concentration) are no longer present and it is therefore safe to say that there will be no new cases of Minamata disease.

Some food and drugs are known to have an effect of excreting methylmercury out of the body.

There are several foods and drugs known to have an effect of having methylmercury leave the body through excrements.
When exposure is noticed, it is critical to perform such excretion treatment as soon as possible.
Such intervention can also be expected to mitigate neurological and other symptoms potentially caused by methylmercury.