Biblatex Printing "ibid" Lowercase at Beginning of Footnote

At the start of sentences you should probably use \Cite, which is defined (in biblatex.def) as

\newrobustcmd*{\Cite}{\bibsentence\cite}

It therefore capitalises the first word it prints (as long as biblatex is able to capitalise that word).

MWE

\documentclass[paper=a5,DIV=7,12pt]{scrartcl}
\usepackage{lipsum}
\usepackage[style=authoryear-icomp,autocite=footnote]{biblatex}
\addbibresource{biblatex-examples.bib}

\begin{document}    
testing.\autocite{malinowski}
testing\autocite{malinowski}.
testing.\footnote{\Cite{malinowski}. I'd like to add: \lipsum[1]} % Prob 2
\end{document} 

---

For your purpose you might want to define a new command (we use LaTeX3's xparse here, so load \usepackage{xparse})

\DeclareDocumentCommand{\longnoteffotcite}{o o m +m}
  {\IfNoValueTF{#2}
     {\footnote{\Cite[#1]{#3}. {#4}}}
     {\footnote{\Cite[#1][#2]{#3}. {#4}}}}

That behaves like \footcite but takes a mandatory long (i.e. allows for \pars and stuff) additional postnote.

The standard postnotes in biblatex do not seem to allow for \pars.

MWE

\documentclass[paper=a5,DIV=7,12pt]{scrartcl}
\usepackage{lipsum}
\usepackage{xparse}
\usepackage[style=authoryear-icomp,autocite=footnote]{biblatex}
\addbibresource{biblatex-examples.bib}

\DeclareDocumentCommand{\longnoteffotcite}{o o m +m}
  {\IfNoValueTF{#2}
     {\footnote{\Cite[#1]{#3}. {#4}}}
     {\footnote{\Cite[#1][#2]{#3}. {#4}}}}

\begin{document}    
testing.\autocite{malinowski}
testing\autocite{malinowski}.
testing.\longnoteffotcite[9]{malinowski}{I'd like to add: \lipsum[1-2]\par Hi}
\end{document}