Urgent, Please help, where can I find worldwide standards of manganese mining?
Your issue is an issue for all types of mining near residential or built up areas, not just manganese mining.
The distance that mines should be from built up areas depends on

the competency of the ground
whether the ground is hard or soft
the type of explosive used - more particularly the energy released by
the explosives used. This influences the blast vibrations produced.
Currently Australian and New Zealand recommendation is a maximum
blast vibration of 10 mm/s in residential areas, preferably less than 2.5 m/s.
the amount of explosives detonated at a time. Many smaller blasts are
usually better than one very large blast.
the presence of geological structures that may preferentially carry
and appear to amplify blast energy

The trouble with laws and standards for such things is they vary between mining jurisdictions. Even within countries, such as the US, Canada and Australia they can vary between states or provinces. Such countries do not have national legislation for the operation of mines. Each state of province is responsible for such laws within its jurisdiction.
In the 1980s, in the State of New South Wales in Australia, to protect lakes and dams from unexpected drainage and also to protect underground coal mines and the people that work in them from water inundation from lakes, dams or other such large stores of surface water a 45 degree angle rule was used.

From the edge of the lake draw a 45 degree line downwards. Where that line intersects the horizontal, or near horizontal, coal seam that defines the closest proximity the mine was allowed to get near the surface lake or dam.

Because of the geometry of a 45 degree triangle both of the shorter sides are the same length. In the case of this rule the distance from the edge of the lake or dam is equal to the depth of mining.
One of the problems with this rule is coal mines in Australia do not use explosives. Coal is mined using cutting machines via longwall mining.
In the City of Ballarat, Australia, gold mining resumed in the 1990s, after the closure of mines during the 1914 to 1918 world war because of a labor shortage. The mine operates underneath the city of 105 000 people.
Under the license to operate, from the State Government of Victoria:

Our licence conditions state that the vibration limit for blasting is 10 mm/sec and that 95% of all blasts must be below 5 mm/sec.

The mine has a self imposed limit of 2.5 mm/s.
Existing underground mine development, in blue, as of July 2020.

Under a proposed expansion to the mine, the newer region will be approximately 50 m below the surface. See the sectional diagram at the end of the webpage. The surface is at elevation RL 1205 and the top of the Nick O' Time Shoot is elevation RL 1150. I suspect this region will under fields or forest.
Generally, for mines under urban environments 100 m is the closest that mines come to the foundations of buildings. This is not primarily due to blasting waves and seismic activity from blasting, but the requirement to maintain a thickness of competent rock beneath buildings to minimize potential for future subsidence.
Factors that are considered in this thickness are:

The strength and competency of the ground below the buildings
The largest size of opening that will be developed underground
Whether the stopes, the chambers from where ore is mined, are
backfilled once the ore has been mined.
If the stopes are backfilled, with what will they be backfilled:
loose waste rock, cemented waste rock, loose sand, cemented sand or
paste fill (larger grained tailings from the processing plant that is
mixed with cement so it resembles toothpaste and is pumped into the
mined stopes).
The degree to which the stopes will be backfilled. Except for the
placement of paste fill, stopes cannot be fully backfilled because of
operational restrictions when other methods are used. There is usually
an air gap of between 2 and 5 m in the top portion of the stope that
cannot be filled.

Backfill prevents the wall of the stopes from collapsing and it minimizes the amount of subsidence that can occur above the stopes.

In your situation, something else to be wary of is exposure to manganese dust from the mine or processing plant. The human body requires small amounts of manganese, but too much can be toxic. Excessive exposure can lead to heath problems with the respiratory tract and/or the brain.

Manganese effects occur mainly in the respiratory tract and in the brains. Symptoms of manganese poisoning are hallucinations, forgetfulness and nerve damage. Manganese can also cause Parkinson, lung embolism and bronchitis. When men are exposed to manganese for a longer period of time they may become impotent.
A syndrome that is caused by manganese has symptoms such as schizophrenia, dullness, weak muscles, headaches and insomnia.

Additional references concerning exposure to excessive amounts of manganese:

National Institutes of Health
Impact of open manganese mines on the health of children dwelling
in the surrounding area
Centers for Disease Control and Prevention (USA)
World Health Organization


Edit 5 September 2020
There is no formula, simple or complex, that will let you calculate how close an active underground mining region can be to buildings on the surface. The reasons for this are:

Geology is complex: different rock types, strength of rock masses
laterally and at depth, geological structures such as
discontinuities, faults and folds.
How the ground propagates blast energy.
The magnitude of the blast energy produced during mining.
Quality of construction of surface buildings: flexibility and
rigidity.

Unlike steel, rock is not uniform in its properties everywhere. Various types of steel are made according to a recipe: some much iron, so much carbon, so much nickel or chromium. Steel is also given different types of treatments when produced, such as hot or cold quenching, forging. All this affects the strength and other properties of various types of steel.
When constantly made to the same recipe each type of steel can be tested to determine its properties. With this knowledge, structural and civil engineering can design a building, or any other structure, anywhere in the world with confidence knowing the steel will always behave the same way. Likewise for mechanical engineers when they design parts for machines.
This cannot be said of geological material, such as rock. Limestone behaves differently to sandstone, which behaves differently to basalt, which behaves differently to komatiite or granite.
Even the same type of rock can behave different in different locations. Discontinuities within rock, oxidation, weathering, the effect of water over prolonged periods of time, the effect of ground stresses can all change how a type of rock will behave in different locations.
Unlike structural and mechanical engineers, mining engineers cannot have the same level of confidence in the properties of the materials (different rock types) they use. With experience they know that a certain type of rock will behave in certain way, but that may not be totally applicable elsewhere.
Because of this, it is not possible to create a formula that can be used everywhere that will state how far an active underground mining region must be from surface buildings.
The other factor which would need to considered is the manner of construction of the buildings near the mine. Buildings that are rigid, made of rock or brick will generally experience more damage, if only just cracked walls, than flexible building made of timber or bamboo.
Flexible buildings can move to certain degree, through swaying,  when subjected to forces such as blasting energy, seismic shocks from natural earthquakes and very strong winds. This movement can absorb some of the disruptive energy and the building remains intact.
Rigid buildings have less opportunity to move when subjected to disruptive forces so they have to absorb more of the disruptive energies and in doing so they are more likely to crack and collapse. This is why buildings in earthquake prone regions (such as Italy), or cyclone/hurricane prone regions (such as northern Australia) are now built according to an earthquake or cyclone/hurricane code where reinforcing steel is utilized to increase flexibility of the building, when completed.
From personnel experience I have seen newer, rigidly made, houses such as the one pictured below,

experience clacked walls and other damage from underground mine blasting where the house was 2.5 km laterally from a mine and the blast was 500 m below the surface. The active mining zone was 1.5 km laterally from the house.
An older, more flexible house, shown below, was only 1 km from the mine and it experienced no damage.