tkz-euclide changing labels and size (triangle, inscribed circle)

You could use options when drawing, such as

\tkzDrawCircle[R,very thick](S,\rSN pt)
\tkzDrawPoints[color=black,shape=circle,fill=black](D,E,F,S)

or set styles, such as by \tkzSetUpPoint and \tkzSetUpLine, which are explained in the tkz-euclide manual.

Regarding the labels, you could set their style via an option to the tikzpicture or by \tikzset, such as

\begin{tikzpicture}[scale=1.5,label style/.style={font=\Large}]

By this, the picture changes to

Stefan'answer is correct. I would like only elaborate some methods. First you can use generally most of the tikz's options, then specific macro for an object (here points) have two versions : tkzDrawPoint,and tkzDrawPoints. If all points use the same style (this is recommended) then you can use tkzDrawPoints else you need to use the first version. Finally I prefer to draw the points at the end of the code.

With your code the result is :

\documentclass{article}
 \usepackage{tkz-euclide}
 \usetkzobj{all}
 \begin{document}
 \begin{tikzpicture}[scale=1.5]
   \tkzInit[ymin=-1,ymax=5,xmin=-1,xmax=5]
   \tkzClip 
   \tkzDefPoint(0,0){A}
   \tkzDefPoint(4,0){B}
   \tkzDefPoint(0,4){C}
   \tkzDefCircle[in](A,B,C)
   \tkzGetPoint{S}
   \tkzGetLength{rSN}
   \tkzDrawPoints(A,B,C)
   \tkzDrawCircle[R](S,\rSN pt)
   \tkzDrawPolygon[very thick](A,B,C)
   \tkzInterLC[R](A,C)(S,\rSN pt) \tkzGetFirstPoint{D}
   \tkzInterLC[R](B,C)(S,\rSN pt) \tkzGetFirstPoint{E}
   \tkzInterLL(B,S)(D,E) \tkzGetPoint{F}
   \tkzDrawSegments[thick,red](D,E)
   \tkzDrawSegments[thick,violet](B,F)
   \tkzLabelPoints[left](D)
   \tkzLabelPoints[above left](C,F)
   \tkzLabelPoints[below right](B)
   \tkzLabelPoints[below left](A,S)
   \tkzLabelPoints[above right](E)
   \tkzMarkAngle[size=0.4 cm](B,F,E)
   \tkzLabelAngle[pos=0.6](B,F,E){\large $x$}
   \tkzMarkRightAngle(B,A,C)
   \tkzDrawPoints(D,E)      
   \tkzDrawPoint[color=black,fill=black](F)  
   \tkzDrawPoint[color=black,fill=violet](S)  
 \end{tikzpicture}
 \end{document}