The primary reason that you don't get links in your \Mycite is that the two commands you use to build it (\citeauthor and \citeyear) do not link to the bibliography. One could redefine these building blocks to link their text and that would sort of resolve the issue here, but I recommend a different approach.
Defining \Mycite as done in the MWE has two huge drawbacks
It can't deal with pre- and postnotes, i.e. the optional arguments of \cite: \autocite[cf.][380]{sigfridsson}
It fails spectacularly when you cite multiple entries at once. Try \Mycite{sigfridsson,worman}.
There are more possible complications that will only become relevant if you use advanced features (citation tracking and counting come to mind). Some of those drawbacks can be worked around easily, some workarounds would be more arduous. But there is a better approach.
In general new citation commands for biblatex should be defined via \DeclareCiteCommand and not by gluing together several high-level citation commands with \newcommand.
So you could try something like
\documentclass{article}
\usepackage[style = numeric, labeldateparts, defernumbers = true, backend = biber, autocite=inline]{biblatex}
\usepackage{hyperref}
\newbibmacro*{cite:authoryear}{%
\printtext[bibhyperref]{%
\iffieldundef{shorthand}
{\ifthenelse{\ifnameundef{labelname}\OR\iffieldundef{labelyear}}
{\usebibmacro{cite:label}%
\setunit{\printdelim{nonameyeardelim}}}
{\printnames{labelname}%
\setunit{\printdelim{nameyeardelim}}}%
\usebibmacro{cite:labeldate+extradate}}
{\usebibmacro{cite:shorthand}}}}
\newbibmacro*{cite:shorthand}{%
\printfield{shorthand}}
\newbibmacro*{cite:label}{%
\iffieldundef{label}
{\printfield[citetitle]{labeltitle}}
{\printfield{label}}}
\newbibmacro*{cite:labeldate+extradate}{%
\iffieldundef{labelyear}
{}
{\printtext[parens]{\printlabeldateextra}}}
\DeclareCiteCommand{\aycite}
{\usebibmacro{prenote}}%
{\usebibmacro{citeindex}%
\usebibmacro{cite:authoryear}}
{\multicitedelim}
{\usebibmacro{postnote}}
\addbibresource{biblatex-examples.bib}
\begin{document}
The first two citations \autocite{sigfridsson} and \autocite{worman}.
The others are \aycite{baez/online} and \aycite{ctan,markey}.
\printbibliography
\end{document}
!["The first two citations [4] and [5]. The others are Baez and Lauda (2004) and CTAN (2006), Markey (2005)." The bibliography is has a label number for all entries.](../../images/183b7aaf8e500a31143426300a3c91a2.webp)
The output in that example is less than ideal, though. All entries get a label number in the bibliography even those which were only cited with author-year labels and author and year are not as prominent in the bibliography as they are with style=authoryear making the entries harder to locate. Additionally, only the choice of the citation command decides the citation format: That requires you to remember which item is to be cited with which command.
If there is a simple rule that governs whether an entry is going to be cited as numeric or author-year then I suggest you look for an automatic solution that uses only one command that decides which format to use on its own. Such a citation scheme can be found in Two different bibliographies with different styles and sortings, Vol.2 where the format is decided by a keyword, but it could also be decided by the entry type or via an ad-hoc (document-dependent) category assignment.
In general I would avoid mixing several citation styles in the same document. It is very unusual to mix styles and it might confuse people at first. There is a good reason why most style guides advocate consistency in citation styles. For some very restricted uses I can see benefits in using different styles, but I'm not sure if what you have in mind really falls into such a category.
Also, the sources can include websites (apart from Arxiv), which is why the authoryear style does not fit for this case.
– DominikR Oct 01 '18 at 11:59