Only \autocite moves trailing punctuation. The chem-acs style loads the option settings autopunct=true and autocite=superscript. So you can achieve the desired inline citation output with \autocite instead of \footfullcite. For the footnotes you can redefine \supercite to \superfullcite from another citation style by Joseph Wright.
\documentclass{article}
\usepackage[style=chem-acs,subentry,citetracker]{biblatex}
\usepackage[colorlinks]{hyperref}
\makeatletter
% http://www.texdev.net/2010/03/08/biblatex-numbered-citations-as-footnotes/
\DeclareCiteCommand{\supercite}[\cbx@superscript]%
{\usebibmacro{cite:init}%
\let\multicitedelim=\supercitedelim
\iffieldundef{prenote}{}{\BibliographyWarning{Ignoring prenote argument}}%
\iffieldundef{postnote}{}{\BibliographyWarning{Ignoring postnote argument}}}
{\usebibmacro{citeindex}%
\usebibmacro{superfullcite}%
\usebibmacro{cite:comp}}
{}
{\usebibmacro{cite:dump}}
\newbibmacro*{superfullcite}{%
\ifciteseen{}{\xappto\cbx@citehook{%
\noexpand\footnotetext[\thefield{labelnumber}]{\fullcite{\thefield{entrykey}}.}}}}
\newrobustcmd{\cbx@superscript}[1]{%
\mkbibsuperscript{#1}%
\cbx@citehook
\global\let\cbx@citehook=\empty}
\let\cbx@citehook=\empty
\makeatother
\addbibresource{biblatex-examples.bib}
\begin{document}
\null\vfill\noindent
New citation \autocite{stdmodel}.
New and recurrent citations \autocite{stdmodel,companion}.
\clearpage
\null\vfill\noindent
New citation \autocite{ctan}.
Recurrent citations from previous and current pages \autocite{companion,glashow,ctan}.
\clearpage
\printbibliography
\end{document}
Here is the output for the first page:
And the second:
Note that this avoids recurrent footnote citations by printing the footnote only the first time the entry is cited. Printing the footnotes at most once on every page can be done, but the solution is relatively messy.
\documentclass{article}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[style=chem-acs,subentry,citetracker,pagetracker=page]{biblatex}
\usepackage[colorlinks]{hyperref}
\makeatletter
% user-level citation command
\DeclareCiteCommand{\supercite}[\cbx@superscript]
{\usebibmacro{cite:init}%
\let\multicitedelim\supercitedelim
\iffieldundef{prenote}{}{\BibliographyWarning{Ignoring prenote argument}}%
\iffieldundef{postnote}{}{\BibliographyWarning{Ignoring postnote argument}}}
{\usebibmacro{citeindex}%
\usebibmacro{cite:super:foot}%
\usebibmacro{cite:comp}}
{}
{\usebibmacro{cite:dump}}
% save current and last inline instcount, save key if seen first on page
\newbibmacro*{cite:super:foot}{%
\xdef\cbx@key{\thefield{entrykey}}%
\ifsamepage{\value{instcount}}{\csuse{cbx@instcount@\cbx@key}}{}{%
\listxadd{\cbx@savelist}{\cbx@key}%
\ifnumequal{\value{cbx@tempcntd}}{0}{%
\defcounter{cbx@tempcntc}{\value{instcount}}%
\loop\ifnum\value{cbx@tempcntc}>0
\ifsamepage{\value{instcount}}{\value{cbx@tempcntc}}
{\ifcsundef{blx@fnpage@\number\numexpr\value{cbx@tempcntc}}
{\setcounter{cbx@tempcntd}{\value{cbx@tempcntc}}}{}%
\stepcounter{cbx@tempcntc}}
{\setcounter{cbx@tempcntc}{0}}%
\repeat}{}}%
\csnumgdef{cbx@instcount@\cbx@key}{\value{instcount}}}
\let\cbx@savelist\@empty
\newcounter{cbx@tempcntc}
\newcounter{cbx@tempcntd}
\setcounter{cbx@tempcntd}{0}
\newrobustcmd*{\cbx@superscript}[1]{%
\global\toggletrue{cbx@supercite}
\mkbibsuperscript{#1}%
\cbx@footnote%
\global\togglefalse{cbx@supercite}}
\let\cbx@savelist\@empty
\newtoggle{cbx@supercite}
\AtEveryCitekey{%
\ifciteseen{}{\csnumgdef{cbx@instcount@\thefield{entrykey}}{-1}}%
\iftoggle{cbx@supercite}{}{\cbx@footnote}}
\AtEveryBibitem{\cbx@footnote}
\AtEveryLositem{\cbx@footnote}
% defer citation footnotes to last inline reference instance on page
\newrobustcmd*{\cbx@footnote}{%
\ifboolexpr{ not test {\ifdefempty{\cbx@savelist}}
and test {\ifnumequal{\value{instcount}}{\value{cbx@tempcntd}}} }
{\cbx@sortlist@init%
\let\do\cbx@do
\dolistloop{\cbx@sortlist}%
\global\let\cbx@savelist\@empty
\setcounter{cbx@tempcntd}{0}}{}}
% print footnotes in 'sorting' order
\def\cbx@do#1{%
\ifinlist{#1}{\cbx@savelist}
{\begingroup
\blx@resetdata
\blx@getdata@cite{#1}%
\blx@setoptions@type\abx@field@entrytype
\blx@setoptions@entry
\blx@execute
\blx@beglang
\iffieldundef{shorthand}
{\gdef\@thefnmark{\printfield{labelprefix}\printfield{labelnumber}}}
{\gdef\@thefnmark{\printfield{shorthand}}}%
\gappto\@thefnmark{\blx@initunit}%
\ifhyperref
{\H@@footnotetext{\blx@driver\abx@field@entrytype}}
{\@footnotetext{\blx@driver\abx@field@entrytype}}%
\blx@endlang
\endgroup}
{}}
% access internal list of sorted entry keys
\def\cbx@sortlist@init{%
\global\letcs{\cbx@sortlist}
{blx@slist@entry@\the\c@refsection @\blx@refcontext@context}}
\let\cbx@sortlist\@empty
\makeatother
\addbibresource{biblatex-examples.bib}
\renewcommand*{\thefootnote}{\fnsymbol{footnote}}
\begin{document}
\null\vfill\noindent
New citation \autocite{stdmodel}.
New and recurrent citations \autocite{stdmodel,companion}.
Vanilla footnote with citation.\footnote{Following \textcite{weinberg}...}
\clearpage
\null\vfill\noindent
New citation \autocite{ctan}.
Recurrent citations from previous and current pages \autocite{companion,glashow,ctan}.
\clearpage
\printbibliography
\end{document}
Here is the output for the first page:
And the second:
