As fas as I know, there is no way to get the Math module without the other modules, so you would need a running LibreOffice in the background. You can use LibreOffice in server-mode. But that goes beyond the answers that you can expect from the “Ask”-forum. You should use the developer IRC freenode #libreoffice-dev for that.
Find the license of LibreOffice in https://www.libreoffice.org/about-us/licenses/
The format, which is specified in ODF for Math formulas, is MathML. But LibreOffice adds it own “StarMath” string to it as annotation and uses this when reopening the file. Other applications will only read the MathML part.
I’m not sure whether LibreOffice Math is the best choice for you, because not all features of MathML are supported. Have you considered to use MathJax? Mozilla has a very good MathML support in its Composer. Have you already talked with Mozilla developers? Are you sure you will use MathML at all?
LibreOffice itself has not “stuff”. It is developed by volunteers and by developers of enterprises, where the enterprises pay the developer to work on LibreOffice. If you want to pay for a special feature, you need to get in contact with such an enterprise. You find some of them on Professional Support | LibreOffice - Free Office Suite - Based on OpenOffice - Compatible with Microsoft
