Best Practice: Package for Mathematical Documents - amsmath and Beyond
multi-question questions don't really fit the site format but..
Do you think that it is Ok to recommend the mathtools package instead of amsmath package. The mathtools package calls the amsmath package and improves it as far as I understand.
Yes
What about the empheq package
It's OK but more of a "contrib" package than mathtools which aims to be a core extension of amsmath. That is if you want that feature it's a perfectly good package to get it, but otherwise no need to mention it.
Is the fixmath package (link) still needed? Can I achieve the ISO conform formatting also with the mathtools mathtools package?
It was never needed, but if you want that style then again it works. Note it is a mistake to think of "ISO conformant mathematics" That isn't how ISO works. IS0 31 is just one possible style guide that was standard for use by one community (in physics mostly) it certainly is almost never followed in mathematics.
Are there other fonts which can be safely be used without running in too much trouble with the availability of symbols and font features
These days you can normally assume people are using a packaged distribution such as texlive or miktex so any font set that is in there will be available or easily installed via package update, which means that there are more choices than in previous eras.
Do you have any further recommendations about good practice
Read a manual before starting, don't use blank lines before a displayed equation, make sure the mathematics is correct not just typeset well:-)
To answer your question 4 about fonts, you can get a good list of Type 1 math fonts usable by PDFLaTeX, with samples, at the LaTeX Font Catalogue. I personally like
\usepackage[osf,slantedGreek]{mathpazo}
This gives you an attractive Palatino clone with excellent coverage. You can combine it with other math symbol packages, such as amssymb, boondox and mathabx. The most comprehensive set of symbols PDFTeX will support, with its limited number and size of math alphabets, is in the stix package, which is based on Times Roman. Another good choice is fourier with Utopia.
In XeLaTeX and LuaLaTex, the unicode-math package supports any OpenType math font: Asana Math, XITS Math, TeX Gyre Pagella Math, Latin Modern Math, Cambria Math, etc. Any Unicode math font will have better coverage than any combination of traditional LaTeX packages. Asana Math is a great replacement for mathpazo. XITS Math is based on Times Roman, and Latin Modern Math is based on the default Computer Modern and the classic glyphs. I personally like how Asana Math and Palatino look, but XITS Math has the most symbols and Latin Modern Math looks the most like classic LaTeX. Several of the TeX Gyre fonts support math: you can compare Pagella to Asana and Termes to XITS. Cambria Math is what Microsoft’s equation editor uses, but for once, they followed a standard and made something that works in other programs; I mention it for the sake of completeness.
I recommend using the unicode-math package for new work, or a font package that loads it: it’s a lot more powerful and flexible than traditional LaTeX, and all new fonts these days are released as OpenType Unicode fonts. Linux Libertine has even removed its support for Type 1. Among other features, unicode-math defines all the commonly-used symbols, including the ones from textcomp, amssymb and tipa. It completely removes the limit on how many glyphs you can support and the need to split them between different math alphabets. It allows you to copy symbols from your PDF and paste them in other applications. It lets you put Unicode symbols directly into your source file. It makes it very easy for you to use any glyph or range of them from any font you want. For example, you could tell it to use your favorite Fraktur font for \mathfrac or your favorite script fonts for \mathscr and \mathcal. And I like to tell it to use the ▮ tombstone symbol from XITS Math at the end of a proof, following the usage of (some of the time) both Paul Halmos, who introduced it, and Donald E. Knuth. But it works well if you just load it without any of that extra setup and is backwards-compatible.