Like Nemo XXX said, Times New Roman is a commercial font, so you are not allowed to freely include it in your ebook and distribute it without acquiring a proper license.
However, I think that you can still freely reference it in your CSS stylesheet without physically incorporating it(1).
Anyway, this presupposes that the font will be installed on the end user's PC or device, which you can't be 100% sure. Granted, Times New Roman is a fairly common font, at least if you don't look beyond Windows machines, but, in example, it is NOT installed by default in many Linux distributions and many e-reader devices.
I think that your best option is to look for an open source font with a free license and directly incorporate it. You really have a lot of alternatives, I'm listing here juts some of the most common ones.
My personal suggestion is to check out the Noto font family, from Google; they are designed to cover all the scripts encoded in the Unicode standard. It is easily one of the most complete and compatible font sets out there, and they are generally good looking and pleasant (this is of course subjective). An alternative, always from Google, is the Droid family, from which Noto is partly derived.
The Liberation and Linux Libertine/Biolinum families are specifically designed to be a free and open substitute to Windows standard fonts such as Times New Roman, Arial and Courier New.
DejaVu, similarly, is a fairly complete set of fonts that is installed by default on many of the main Linux distributions.
As Nemo XXX suggested, Charis SIL is a good and fairly complete font (and, if you ask me, also more distinctive and better looking that the old plain and kinda boring Times New Roman). Another option, always from SIL International, is Gentium.
(2017-06-22 EDIT) Martel and Martel Sans fonts are specifically designed to cover Latin and Devangari characters.
I'm not really familiar with Devangari (or any other non-latin) script, so you should check these alternatives yourself and see if they suit your needs. I can't guarantee that all the fonts that I've listed include the characters that you need to display, I've just pointed out some of the major open source font projects, I leave it to you to make your tests.
About the samples: I've tried to open both the ePub and PDF that you have provided, they are BOTH displayed with latin characters, even the non-english text.
1) Please note that I'm not a lawyer and I'm just saying this out of common sense, do your research accordingly.