For Question 2: In addition to Kellerhals' lower bounds on $\epsilon(n)$, there is an absolute constant $C>0$ such that
$$
\epsilon(n)\le \frac{C}{\sqrt{n}},
$$
see Proposition 5.2 in

<cite authors="Belolipetsky, Mikhail">_Belolipetsky, Mikhail_, [**Hyperbolic orbifolds of small volume**](https://arxiv.org/abs/1402.5394), Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. II: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-805-6/hbk; 978-89-6105-803-2/set). 837-851 (2014). [ZBL1373.22017](https://zbmath.org/?q=an:1373.22017).</cite>

The paper is also available in arXiv [here](https://arxiv.org/pdf/1402.5394.pdf).