To remove the header on the next pages use
\setkomavar{nexthead}{}
For the second problem use a \parbox inside firstfoot
\setkomavar{firstfoot}{\usekomafont{pageheadfoot}\usekomafont{pagefoot}%
\parbox[t]{\textwidth}{%
\rule[3pt]{\linewidth}{.4pt} \\
\begin{tabular}[t]{l@{}}%
Super Man\\
Super Straße 30\\
12345 Super Town
\end{tabular}%
\hfill
\begin{tabular}[t]{l@{}}%
Telefon: +49123456789\\
super.man@gmail.com\\
\end{tabular}%
\hfill
\begin{tabular}[t]{l@{}}%
Bankverbindung: \\
IBAN: DEXX XXXX XXXX XXXX XX\\
BIC: XXXXXXXXXXXXX
\end{tabular}%
}%
}%
Note that firstfoot is a variable too and command \firstfoot is depreciated.
But the footer will still have a different position and width on the two pages:

Pagestyle plain with package scrlayer-scrpage
I would load package scrlayer-scrpage and use a plain page style on all pages.
The following examples uses the normal plain style. Only the footsepline is a bit shifted upwards.
\documentclass[
firstfoot=false,%<- no first foot
footheight=48pt
]{scrlttr2}
\usepackage{blindtext}% dummy text
\usepackage[footsepline,plainfootsepline]{scrlayer-scrpage}
\ModifyLayer[
addvoffset=-1ex
]{plain.scrheadings.foot.above.line}% shift the footsepline up
\addtokomafont{pagefoot}{\normalfont\footnotesize}
\clearpairofpagestyles
\cfoot*{
\begin{tabular}[t]{l@{}}%
Super Man\\
Super Straße 30\\
12345 Super Town
\end{tabular}%
\hfill
\begin{tabular}[t]{l@{}}%
Telefon: +49123456789\\
super.man@gmail.com\\
\end{tabular}%
\hfill
\begin{tabular}[t]{l@{}}%
Bankverbindung: \\
IBAN: DEXX XXXX XXXX XXXX XX\\
BIC: XXXXXXXXXXXXX
\end{tabular}%
}
\pagestyle{plain}
\usepackage{xpatch}
\xapptocmd\opening{\thispagestyle{plain}}{}{}% <- first pages will have pagestyle plain too
\begin{document}
\setkomavar{fromname}{Name}
\setkomavar{firsthead}{It is still possible to set a firsthead.}% <- firsthead still works
\begin{letter}{Addr}
\opening{}
\Blindtext
\closing{}
\end{letter}
\end{document}

But you can also change the vertical position and the width of the footer to your needs. Here is an example similar to the normal firstfoot settings.
\documentclass[
firstfoot=false,%<- no first foot
footheight=48pt
]{scrlttr2}
\usepackage{blindtext}% dummy text
\usepackage[footsepline,plainfootsepline]{scrlayer-scrpage}
\KOMAoptions{footwidth=\useplength{firstfootwidth}}
\ForEachLayerOfPageStyle*{plain.scrheadings}{%
\ifstrstart{#1}{plain.scrheadings.foot}{%
\ModifyLayer[
voffset={\useplength{firstfootvpos}-1em}
]{#1}
}{}
}% shift the footer down
\ModifyLayer[
addvoffset=-1ex
]{plain.scrheadings.foot.above.line}% shift the footsepline up
\addtokomafont{pagefoot}{\normalfont\footnotesize}
\clearpairofpagestyles
\cfoot*{
\begin{tabular}[t]{l@{}}%
Super Man\\
Super Straße 30\\
12345 Super Town
\end{tabular}%
\hfill
\begin{tabular}[t]{l@{}}%
Telefon: +49123456789\\
super.man@gmail.com\\
\end{tabular}%
\hfill
\begin{tabular}[t]{l@{}}%
Bankverbindung: \\
IBAN: DEXX XXXX XXXX XXXX XX\\
BIC: XXXXXXXXXXXXX
\end{tabular}%
}
\pagestyle{plain}
\usepackage{xpatch}
\xapptocmd\opening{\thispagestyle{plain}}{}{}% <- first pages will have pagestyle plain too
\begin{document}
\setkomavar{fromname}{Name}
\setkomavar{firsthead}{It is still possible to set a firsthead.}% <- firsthead still works
\begin{letter}{Addr}
\opening{}
\Blindtext
\closing{}
\end{letter}
\end{document}
