Subcategories of T1, Hausdorff and TD spaces are reflective subcategories of Category *Top*. How do I construct a T1, Hausdorff and TD reflections  to show that subcategories of T1, Hausdorff and TD spaces are reflective subcategories of Category Top?
The T0 reflection is just the T0 quotient of a space X. What about the others?

This question and its answers talk in detail about the Hausdorff reflection.
The $T_1$ reflection of $X$ is the quotient under the intersection of all equivalence relations on $X$ that have closed equivalence classes, see the post here with an attempted proof (the previous one has the statement). 
My details: Let $X$ be any space and define $$\mathcal{C} = \{S \subseteq X \times X: S \text{ is an equivalence relation and } \forall x \in X: [x]_S \text{ closed in } X\}$$ where $[x]_S$ is the class of $x \in X$ under $S$.
This is a non-empty set of equivalence relations as the trivial relation $R= X \times X$ is in $\mathcal{C}$. As the intersection of any family of equivalence relations is again an equivalence relation $R= \bigcap\{S \in \mathcal{C}\}$ is well- defined. As for any $x$ we have $$[x]_R = \bigcap \{[x]_S: S \in \mathcal{C}\}$$ and intersections of closed sets are closed, we have that $R$ also has the property that all classes are closed and so $X/R$ is a well-defined $T_1$ space in the quotient topology (with quotient map $q: X \to X/R$ defined as usual by $q(x)= [x]_R$). This $(X/R,q)$ is the $T_1$-reflection of $X$: let $Y$ be any $T_1$ space and $f: X \to Y$ continuous. Then $R_f = \{(x,x') \in X \times X: f(x)=f(x')\}$ is an equivalence relation and as $[x]_{R_f} = f^{-1}[\{f(x)\}]$, $R_f \in \mathcal{C}$, and so $R \subseteq R_f$, which implies that if $[x]_R =[x']_R$ we have that $f(x) = f(x')$ too, so that $\tilde{f}([x]_R) = f(x)$ is well-defined and continuous as $q^{-1}[\tilde{f}^{-1}[O]] = f^{-1}[O]$ for all $O$ and $X/R$ has the quotient topology w.r.t. $q$. It's clear that $\tilde{f}$ is unique. 
That same linked thread claims that $T_D$ is not reflective because $S_2^{\aleph_0}$, where $S_2$ is the Sierpi&nacute;ski two-space, is not $T_D$. More is explained in the introduction of this paper.
