For your three issues the solutions are actually quite short.
The only format with quotation marks is title for "dependent"/@in...-like entry types
\DeclareFieldFormat
[article,inbook,incollection,inproceedings,patent,thesis,unpublished]
{title}{#1\isdot}
Your second request could be dealt with as in biblatex: How to remove the parentheses around the year in authoryear style?, but I used the direct approach.
\renewbibmacro*{date+extrayear}{%
\iffieldundef{labelyear}
{}
{\setunit{\addperiod\space}%
\printtext{%
\iffieldsequal{year}{labelyear}
{\printlabeldateextra}%
{\printfield{labelyear}%
\printfield{extrayear}}}}}
For your third issue we can use the code from the question in Biblatex: have "and" in the citation but "&" in the bibliography, no need for separating citations and bibliographies
\DeclareDelimFormat{finalnamedelim}{%
\ifnumgreater{\value{liststop}}{2}{\finalandcomma}{}%
\addspace\&\space}
Full MWE with a bit of bonus code
\documentclass[british]{article}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=authoryear,backend=biber]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{merdith_full-plate_2017,
Author = {Merdith, Andrew S. and Collins, Alan S. and Williams, Simon E. and Pisarevsky, Sergei and Foden, John D. and Archibald, Donnelly B. and Blades, Morgan L. and Alessio, Brandon L. and Armistead, Sheree and Plavsa, Diana and Clark, Chris and M{\"u}ller, R. Dietmar},
Date = {2017},
Title = {A full-plate global reconstruction of the Neoproterozoic}}
@article{england_active_1997,
Author = {England, Philip and Molnar, Peter},
Date = {1997},
Number = {5338},
Pages = {647--650},
journal = {Science},
Title = {Active deformation of Asia: from kinematics to dynamics},
Volume = {278}}
}
\end{filecontents}
\addbibresource{\jobname.bib}
% issue 1
\DeclareFieldFormat
[article,inbook,incollection,inproceedings,patent,thesis,unpublished]
{title}{#1\isdot}
% issue 2
\renewbibmacro*{date+extrayear}{%
\iffieldundef{labelyear}
{}
{\setunit{\addperiod\space}%
\printtext{%
\iffieldsequal{year}{labelyear}
{\printlabeldateextra}%
{\printfield{labelyear}%
\printfield{extrayear}}}}}
% issue 3
\DeclareDelimFormat{finalnamedelim}{%
\ifnumgreater{\value{liststop}}{2}{\finalandcomma}{}%
\addspace\&\space}
% bonus
\renewbibmacro{in:}{%
\ifentrytype{article}{}{\printtext{\bibstring{in}\intitlepunct}}}
% (from https://tex.stackexchange.com/q/10682/35864)
\DeclareFieldFormat[article,periodical]{volume}{\mkbibbold{#1}}
\DeclareFieldFormat[article,periodical]{number}{\mkbibparens{#1}}
\renewbibmacro*{volume+number+eid}{%
\printfield{volume}%
\printfield{number}%
\setunit{\addcomma\space}%
\printfield{eid}}
\renewcommand*{\bibpagespunct}{\addcolon\space}
\DeclareFieldFormat[article]{pages}{#1}
\begin{document}
\cite{merdith_full-plate_2017} and \cite{england_active_1997}
\printbibliography
\end{document}
Keks Dose makes the good point in the comments that not only do the legal systems differ from country to country so do their citation practices.
The styles listed below come mainly from an English/American common law perspective.
Styles with support for legal citations
A handful of biblatex styles have some kind of support for legal citations with @jurisdiction and @legislation (I only listed styles that I consider to be of recent vintage, i.e. updated after the release of biblatex v3.3 in 2016)
biblatex-abnt aliases both to @article.
biblatex-apa defines the types @legislation, @legadminmaterial, @legal and @jurisdiction. Some (commented) example entries can be found in biblatex-apa-test-references.bib. See also §4.2.5 Legal Entry Types of the biblatex-apa documentation.
biblatex-bath has support for UK legislation and parliamentary reports (@legislation) as well as EU legislation and reports (as @legislation) and case reports (@jurisdiction). See §§4.8-4.10 of the documentation.
biblatex-chicago offers the types @jurisdiction, @legal and @legislation following CMS/Bluebook recommendations.
biblatex-oxref (by the author of biblatex-bath) also offers support for legal sources mimicking OSCOLA with a few minor differences. See §10 Legal references of the style documentations (here oxyear) For the author-year style oxyear the author notes
Since legal references are usually cited using footnotes, how oxyear should behave is not well defined. As a result, I have not configured it to do anything fancy: the full reference will be formatted just the same as with oxnotes, and citations will typically be title–year using parentheses in the usual way.
biblatex-philosophy has experimental support for @jurisdiction.
oscola has support for much of the English-speaking world.
biblatex-apa, biblatex-bath, biblatex-oxref's oxyear style and biblatex-chicago's authordate will be of particular interest since those styles usually follow an autho-year scheme and are otherwise not focused on legal citations.
As far as I can see biblatex-bath and biblatex-oxref can get away with not modifying the citation commands significantly (a few delimiters are modified but the cite bibmacro itself not), biblatex-chicago has has dedicated macros set up for legal citations. All styles have dedicated drivers and supporting infrastructure for the accepted entry types.
There were also dedicated styles for German legal citations, Swiss legal style and French legal citations, but these styles have not been updated recently and will probably not work as intended any more. A more recent French style is https://github.com/ienissei/frenchlaw
2020 Update The German style biblatex-juradiss got an emergency update so that it at least works again. There are also the two new styles biblatex-jura2 and biblatex-german-legal.
Write your own legal references
Depending on the output you expect and the input you find reasonable the work you may have to do can vary.
Bibliography
I think it is fair to assume that you will have to write a dedicated bibliography driver for @legislation and @jurisdiction. Mapping to a standard driver like @article, @misc or @book is probably not enough for you.
The general approach to writing a bibliography driver as shown in Creating Entry in Bibtex for Executive Orders and How can I create entirely new data types with BibLaTeX/Biber? is still valid. I would definitely prefer bibstrings over hard-coded text in macros and would usually try to avoid \printtext and try to use \DeclareFieldFormat as much as possible (but I guess to some extent that is just a matter of taste). As we are all painfully aware there are no comprehensive "introduction to writing a biblatex style" or "my first bibdriver" available (yet?), so I would usually recommend to learn by looking at examples. Naturally you would start with the standard drivers, but I believe most of the styles listed above can also be used to learn best practices - if you keep in mind that some of them need to implement a complicated set of rules and so some tricks are required once in a while.
You may also have to add certain fields to the default data model if you feel that the available fields don't cover everything you need. (biblatex-oxref adds a few non-standard fields for case reporting for example.) See Add field "tome" to biblatex entries.
With a bit of care those two things can happen almost independent of the style that is later used.
Citation
For citations the situation is not as clear.
As biblatex-oxref and biblatex-bath demonstrate it might not actually be necessary to modify the cite macros, it can be enough to use existing features like labeltitle, labeldate and a few modifications of their behaviour to obtain acceptable citation output. But depending on the rest of your style and your input it may be necessary to change the cite macro to incorporate legal citations. This gets harder to pull off in a way that is independent of the used citation style. If you use a complicated style such as authoryear-icomp some care needs to be taken to make sure legal citations interact with the various features of the style in a reasonable way.
A dedicated \lawcite command might be an option that avoids messing with heavily style-dependent citation commands, but it does not feel as nice to me.
Best Answer
There is a biblatex style for Oscola: oscola. It requires biblatex 2.0 (or later) and bibtex 1.0 (or later).