tikz: nodes overlapping with edges on graph

Question

I'm trying to reproduce a graph from a paper using Tikz, the graph that I'm trying to reproduce is the following:

But without the horizontal curved line and brackets on the left subtree. So far, this is what I get:

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}

\tikzset{
    treenode/.style = {align=center, inner sep=0pt, text centered,
        font=\sffamily\Large\bfseries, text width=5cm},
    burned/.style = {treenode, circle, white, draw=red, fill=red, text width=1.5em, very thick},
    saved/.style = {treenode, circle, white, draw=green, fill=green, text width=1.5em, very thick},
    untouch/.style = {treenode, circle, white, draw=gray, fill=gray, text width=1.5em, very thick}
}

\begin{document}

\begin{tikzpicture}[auto, node distance=2cm, thick]
% nodes
\node[burned](1){F};
    \node[saved](2) [below left of=1] {S};
    \node[untouch](3) [below left of=2] {};
    \node[untouch](4) [below right of=2] {};
    \node[burned](5) [below of=1] {B};
    \node[burned](6) [below right of=1] {B};
    \node[saved](7) [below of=5] {S};
    \node[burned](8) [below of=6] {B};
    \node[untouch](9) [below of=7] {};
    \node[saved](10) [below of=8] {S};
    \node[untouch](11) [below of=9] {};
    \node[untouch](12) [below of=11] {};
    \node[untouch](13) [below of=10] {};
    \node[untouch](14) [below of=13] {};

%edges
\path
    (1) edge node [right] {} (2)
        edge node [below] {} (5)
        edge node [left] {} (6)
    (2) edge node [right] {} (3)
        edge node [right] {} (4)
    (5) edge node [below] {} (7)
        edge node [left] {} (8)
    (7) edge node [below] {} (9)
    (9) edge node [below] {} (11)
    (11) edge node [below] {} (12)
    (6) edge node [right] {} (7)
        edge node [below] {} (8)
    (8) edge node [below] {} (10)
    (10) edge node [below] {} (13)
    (13) edge node [below] {} (14);
\end{tikzpicture}

\end{document}

Which produces the following graph:

So, basically I have three questions:

• Is there any way to avoid the overlapping between the edges and nodes?
• Also, there is any way to get the nodes from the same level to be aligned? (Like in the graph of the paper)
• There is another LaTex package or tikz library with a more intuitive syntax to draw graphs (i.e. graphs with edges/nodes)? Maybe something similar do Graphviz dot syntax.

Answer 1

Probably someone will suggest using forest for this kind of graph. It will be a good suggestion. But while waiting for it, you can start using positioning library and its =of (instead of of=) syntax.

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}
\usetikzlibrary{positioning}

\tikzset{
    treenode/.style = {align=center, inner sep=0pt, text centered,
        font=\sffamily\Large\bfseries, text width=5cm},
    burned/.style = {treenode, circle, white, draw=red, fill=red, text width=1.5em, very thick,sibling distance=30mm},
    saved/.style = {treenode, circle, white, draw=green, fill=green, text width=1.5em, very thick,sibling distance=15mm},
    untouch/.style = {treenode, circle, white, draw=gray, fill=gray, text width=1.5em, very thick,sibling distance=7.5mm}
}

\begin{document}

\begin{tikzpicture}[auto, thick, on grid, ]
% nodes
\node[burned](1){F};
    \node[saved](2) [below left = 1 and 2 of 1] {S};
    \node[untouch](3) [below left = 1 and 1 of 2] {};
    \node[untouch](4) [below right = 1 and 1 of 2] {};
    \node[burned](5) [below = 1 of 1] {B};
    \node[burned](6) [below right = 1 and 2 of 1] {B};
    \node[saved](7) [below = of 5] {S};
    \node[burned](8) [below = of 6] {B};
    \node[untouch](9) [below = of 7] {};
    \node[saved](10) [below = of 8] {S};
    \node[untouch](11) [below = of 9] {};
    \node[untouch](12) [below =of 11] {};
    \node[untouch](13) [below = of 10] {};
    \node[untouch](14) [below = of 13] {};

%edges
\path
    (1) edge node [right] {} (2)
        edge node [below] {} (5)
        edge node [left] {} (6)
    (2) edge node [right] {} (3)
        edge node [right] {} (4)
    (5) edge node [below] {} (7)
        edge node [left] {} (8)
    (7) edge node [below] {} (9)
    (9) edge node [below] {} (11)
    (11) edge node [below] {} (12)
    (6) edge node [right] {} (7)
        edge node [below] {} (8)
    (8) edge node [below] {} (10)
    (10) edge node [below] {} (13)
    (13) edge node [below] {} (14);
\end{tikzpicture}

\end{document}

Update: forest version.

\documentclass[a4paper,12pt]{article}
\usepackage{forest}

\tikzset{
    treenode/.style = {align=center, inner sep=0pt, text centered,
        font=\sffamily\Large\bfseries, text width=5cm},
    burned/.style = {treenode, circle, white, draw=red, fill=red, text width=1.5em, very thick,sibling distance=30mm},
    saved/.style = {treenode, circle, white, draw=green, fill=green, text width=1.5em, very thick,sibling distance=15mm},
    untouch/.style = {treenode, circle, white, draw=gray, fill=gray, text width=1.5em, very thick,sibling distance=7.5mm}
}

\begin{document}

\begin{forest}
[F,burned
    [S, saved, , for descendants={untouch}
        [][]]
    [B, burned, name=B1
        [S, saved, name=S1, for descendants={untouch} [[[]]]]]
    [B, burned, name=B2
        [B, burned, name=B3 [S, saved, , for descendants={untouch} [[]]]]]]
    \draw (B1)--(B3) (B2)--(S1);
\end{forest}
\end{document}