I’ve had to use a variety of fonts with LaTeX in the past; some proprietary, some not. These include Avenir, Lyon Text, Helvetica, various monospaced fonts and most recently Adobe Garamond. The font foundry (in your case, HF&J) should have no effect on how you can use them in LaTeX. I don’t think I have any experience with HF&J in particular.
If you have an OpenType font installed on your system (such as one accessible in the drop down menus in Microsoft Word), then XeLaTeX can see it and use it.
There are two packages that are good for this: fontspec and mathspec. Both require XeLaTeX (I think you can use XeTeX, but never tried it myself). Edit: as J.C. Salomon points out in the comments, you can also use LuaLaTeX. I was confusing my personal use of XeLaTeX as being the exclusive configuration.
The fontspec package allows you to use any OpenType font in a LaTeX document, by adding the lines
\usepackage{fontspec}
\setmainfont{Requiem}
The different options you can use with regard to ligatures, fall back fonts, defining new font styles and so on are quite extensive, and described fully in the fontspec documentation. I recommend reading it, it’s not too long. (This is where you change stuff like the font you use for digits, Greek characters, etc.)
The second package, mathspec, is a superset of fontspec with some options for mathematical fonts. For example, you can customise the font that operations like \sin and \log are printed in. Again, I recommend reading the package documentation, for details, which covers it better than I can.
If you’re typesetting maths, then you want to use mathspec. Otherwise fontspec should be fine for you. The two packages are very similar, so if you start using fontspec and find you really need the features of mathspec, then changing is very easy.
To answer your three questions directly:
- I haven’t had any major issues with the custom fonts that I’ve ever used. I’ve never used HF&J fonts (as far as I remember), but I don’t think it should cause any problems.
- Maths characters usually default to the Computer Modern symbols unless told otherwise. In
mathspec you can choose which parts of a typeface to use, so you can choose the digits from Requiem, and Greek characters from Times (for example). Section 4 of the mathspec documentation. Personally I quite like the SIL fonts for Greek.
- I don’t think pdfLaTeX can handle custom fonts as easily; most people I know use XeLaTeX and LuaLaTeX for the job, and that works well for them.
