How is the force calculated when the speed is constant? Is this equation correct? F = m.s Newton's first law does not apply in frames of inertial references?
Speed is constant precisely because there is no force. This is the first law of Newton Yes it does So-called inertial frames are defined by the fact that for objects in relative motion, Newton's first law applies equally to both. Or if you prefer, to any object whatever at rest relative to one set of coordinates, there exists other coordinates relative to which it is in constant motion. This preserves Newton's 1st law in Relativity
I have just explained. If there exist a coordinate set relative to which a body can be considered to be at rest, and if there exist an equally valid coordinate set relative to which the same body can be considered to be in motion, then these two coordinates sets are related by a coordinate transformation which is simple algebra and has nothing, repeat NOTHING to do with forces.
Which force? The net force on an object? If the speed is constant, then the object is not accelerating, and therefore by Newton's second law $F_{net}=ma=0$. What are $m$ and $s$ in that equation? An inertial frame is defined to be one in which Newton's first law applies. Bodies don't need a reason to move. Newton's first law says that a body will remain at rest or keep moving in a straight line at constant speed unless there is a net force on it. Do you mean: is $4m^2 >4m$? Do the algebra! $4m^2 - 4m > 0$ $\Rightarrow 4m(m-1)>0$ $\Rightarrow m(m-1)>0$ This is true if $m<0$ or $m>1$.
This is true, but it isn't enough to define what an inertial frame is. Two objects accelerating side-by-side at the same rate will remain at rest with respect to one another, but neither of them will be in an inertial frame.
This has already been answered if it is assumed that m is a variable, or stand-in for an unknown number. However if m is meant to be a unit of measure, such as meters, then the question is meaningless, as you are trying to compare two different types of measure, linear distance and area. This makes no sense.
Just to expand a little on what NotEinstein said... Mass times speed would have units like $kg.m.s^{-1}$, but force has units of $kg.m.s^{-2}$. Therefore, force cannot equal mass times speed.