What are the important essential softwares a mechanical engineering student should have some grip on?

Here's a list of software generally used by Mechanical Engineers.

General: MATLAB, LaTEX, R (programming language)
Irrespective of your field, this stuff is useful and is generally expected from Mechanical Engineers. As a matter of fact, the last two are recommended to any engineer/professional as they come in handy while making presentations and statistical models.

Design: CATIA, SolidWorks, Pro-E
Every Mechanical Engineer is expected to have a good grip on designing. They use it heavily in most of the fields like Automobile Engineering, Aerospace Engineering, Tool Design, etc. Also with the advancement of Rapid Prototyping and 3-d Printing, they are becoming more visible to the outer world as one can see how exactly your product looks like in just a few hours.

Finite Element Analysis: Ansys, Fluent
People who are into Structural Analysis, Aerodynamics or Fluid Dynamics should have an idea about these. It is particularly useful for students participating in competitions like SAE-Baja as it helps in deciding the shape of the members, the stresses on them, impact of collision, etc. 

Programming: C++, Python
At least one programming language is necessary for any engineer. It doesn't have to do anything with his/her profession but its just good to sharpen your grey cells once in a while. They are used in areas like Robotics, Artificial Intelligence and Control Theory.

Instrumentation: LabView
A Graphical Programming Language, it is very easy to get a hang of it and is pretty interesting too due to its GUI. It is particularly useful in simulation and testing the control and processing part of a system.

How are F1 engines are so powerful?

F1 engines are powerful despite having a small displacement because of some of the reasons below :

1. Ultra Light Engine parts :

All the moving parts of the engine have an inertia associated with them . The lighter the parts are designed , the inertia of the system reduces and this helps to develop more power . The moving or reciprocating parts such as pistons , connecting rods , camshafts , crankshaft are made of alloys which reduce the weight without compromising on strength . Generally aluminium - chromium alloys are used .

2. Size optimization :

Along with using light materials , engineers also considerably reduce size which further contributed to reduction in mass and reduction in the inertia of the system . The image juxtaposes a normal road car piston to a formula 1 piston . The optimization in size is evident from the image. It is possible to do such things as long life of engine is not a parameter in Formula 1 . The engine is designed to last maximum for a season of 19-20 races with an average of about 600 km running per race .

3. High RPM :

The break horse power (BHP) produced by the engine is given by the formula :

BHP = 2*pi*N*T/60
where
N=RPM
T=Torque

So, naturally to produce more power you need either high torque or high RPM . In Formula 1 engine , both are increased to get maximum overall output .
In our road cars usually redline is around 3000-4000 RPM . Even in high end cars like Ferrari Berlinetta and Lamborghini Aventador the engine revs to around 8000-9000 RPM . But F1 engines are clocked at around 16000-18000 RPM range .

4. Stroke to Bore Ratio :

It is the ratio of length of travel of each piston from top dead centre to bottom dead centre divided by the diameter of the cylinder . Generally a Stroke to Bore ratio of about 0.8-1.2 gives optimum efficiency . This factor is dependent on Heat transfer of flame through cylinder , scavenging effects , detonation and knocking tendencies . 
In Formula 1 however , power is of supreme importance hence the engines have a Stroke-bore ratio in the range of 0.4-0.5 . This improves the power but reduces engine efficiency . Also , this increases tendency of detonation and especially knocking which is counter balanced by using High Octane Fuel .

5. Higher Injection Pressure :

In our normal cars it is close to 150 bar but in the recent formula 1 engine it is 500 bar . Higher Injection pressure again contributed to more effective burning in a short span of time , remember to have an engine running at 16000 RPM , combustion time per stroke is very less , therefore increase in injection pressure is must to achieve such high engine speeds .

Law of conservation energy according to NOETHER'S THEOREM.

Conservation of energy is, perhaps, the most solidly established law of physics.  It is not violated by any known process.

The question of "what is energy" was answered in a definitive way by Emmy Noether, a woman who Einstein called one of the greatest mathematicians of all time.  She showed that if you knew the equations of physics (they could by Maxwell's equations, or relativity, or anything else) then you could find a combination of your parameters (typically velocity, position, mass, etc.) that would not change with time. This method gave the quantity that she recognized was "energy" in all previous theories.  Her work is called "Noether's Theorem"  and you can look it up on Wikipedia.  When physicists come up with a new theory, they calculated the energy by using Noether's theorem.

In quantum physics, energy is conserved.  However, when you look at the equations you derive, it often appears that energy is not conserved in the details of the process.  For example, in "tunneling" the particle appears to be inside the potential barrier.  But that is only a way of looking at the equations; for the actual observables, the energy is indeed conserved. You don't actually observe the particle when it is inside the barrier, presumably violating energy conservation.

The uncertainty principle says that when you are about to measure a state, you will not know exactly what energy you will observe.  Yet the conservation of energy is still absolute.  If you put in a precisely known amount of energy, then what you will observe will be that energy, made uncertain by the process of measurement which could disturb that value.

The photo of  EMMY NOETEHR is in below link.

https://qph.is.quoracdn.net/main-qimg-2a1743c09d7e6b4af500fa2fe4890b5b?convert_to_webp=true

If viscosity decreases with increase in temperature, why is lava so viscous?

Viscosity for a particular substance gets lower as the temperature increases, but one substance may have a much different viscosity from another substance at the same temperature.  For instance, honey is more viscous than water at room temperature.  The viscosity will go down for both liquids as temperature increases, but the honey will still be more viscous than the water. 

Lava happens to be very viscous even when very hot.  But still, its viscosity will get smaller when the temperature goes up. 

What is convection,conduction,radiation?

Conduction:
 it is the mode of heat transfer particularly in solids and also for liquid at rest. In this mode of heat transfer, the heat transfers from one atom to its neighbouring atom through molecular vibrations. At molecular level, First heat energy of a higher energy level  molecule converts to vibrating kinetic energy and this kinetic energy is transferred to neighbouring atoms and so on. again process repeats until the temperature difference between two neighbouring  atoms is zero. 

Convection:
This mode of heat transfer particularly occurs in fluids in motion. That is in both liquids and gases that are in motion. This mode of heat transfer occurs due to transfer of energy through bulk mass. 
In detail whenever there is temperature difference in a fluid, density difference occurs and motion of fluid starts as lower density fluid attempts to reach top of the fluid. During this motion mass and energy transfer occurs thus heat transfer takes place. 

Radiation:
In this mode heat can transfer even through vacuum. Heat transfer occurs as quantum packets or light energy. This is the mode by which we receive solar energy from sun.