Take a look at my Garava Font.
I think you will find that all of those characters are available, except for the letters with vertical macron accent, but a vertical macron combining diacritical mark is included. Small Capital N is included too.
For typing, you should be able to find an existing keyboard for Pinyin, but if not you can use the Microsoft Keyboard Layout Creator (freeware), which i used to create my keyboards for Pali.
Garava is released under GNU license agreement. It can be renamed and modified as long as the license agreement is retained and passed on to anyone who wants to use or modify your Pinyin version.
Times New Roman is a copyrighted font. There are any number of dubious versions of it around. It is not the best font for all publications, as it has been overused.