Radius of Turn Query
The difference in headings gives you the number of degrees you need to turn. The distance between the two points then becomes a secant to the turning circle which should give you the turn radius by applying some basic geometry. I assume that the turn starts on point 1 and ends on reaching point 2. Like this:

Now you first need to calculate the turn radius, using the equation for secant length: Start with the difference between the two headings and call that angle $\varphi$. Then the difference between two points $s$ is $$s = 2\cdot r \cdot sin\frac{\varphi}{2}$$
Since you know $s$, you can calculate the turn radius $r$ by a simple transformation: $$r = \frac{s}{2\cdot sin \frac{\varphi}{2}}$$
Now you need to check whether the airplane will be able to turn with that radius. This depends on wing loading $\frac{m}{S}$, density of air $\rho$ and maximum lift coefficient $c_{L_{max}}$, and the equation for the minimum turn radius is $$r_{min} = \frac{2\cdot m}{c_{L_{max}}\cdot S \cdot \rho}$$
Compare both values of $r$ and check if $r &gt; r_{min}$. Then the turn is physically possible.
Now I only hope that this is really what you asked. Your question leaves a lot of room for interpretation.

EDIT: @amarender has updated the question. Now the heading is identical at all intermediate points, and below is one of many possible solutions (blue line):

I indicated with pie segments where the turns are; of course, the one single turn condition has to be interpreted as one turn per intermediate point. The sections between the turns are straight, and all bring the aircraft closer to the destination if the heading at the intermediate points is identical to the heading from target to destination.
When do we have a condition where a solution is not possible? Only if the points are too close together to satisfy the condition of the minimum turning radius. By rotating the coordinate system such that the desired heading at the points is parallel to the x axis, this is easier to show:

The distance between two points in the direction of the desired heading $\Delta x$ must not be smaller than the diameter of the minimum possible circle ($2\cdot r_{min}$) using the equation above. The green line above is for $\Delta x &gt; 2\cdot r_{min}$, and the red line for the boundary condition $\Delta x = 2\cdot r_{min}$. To be precise, the equation above does not put a limit on the maximum load factor $n_{z_{max}}$ - if this needs to be considered, the minimum radius is:
$$r_{min} = \frac{2\cdot \frac{n_{z_{max}}}{\sqrt{n^2_{z_{max}}-1}}}{c_{L_{max}}\cdot \frac{S}{m} \cdot \rho}$$
Things get more complicated when the heading at the points is different from the heading from the source to the destination. Then $\Delta y$ becomes important as well, and when it gets large relatively to $\Delta x$, the straight connection between turns will point away from the target very soon.