Is the nature of LibreOffice such that I can write extensions and charge for their use or is it a given that everything must be open source including the intellectual property of the extension?
You mix concepts. Open source does not require that everything is for no cost. See e.g. FSF’s view on selling free software.
Wrt license requirements imposed on extensions (e.g., based on them using SDK), you need to consult at legal@documentfoundation.org to be on the safe side. However, in any case, I’m sure that your extensions may made be closed-source, e.g. if you use AOO’s SDK which uses Apache license.
I’m by no means a lawyer, so this is not legal advice of any kind.
LibreOffice and its SDK are licensed under the Mozilla Public License v2.0 (MPLv2), see Licenses | LibreOffice - Free Office Suite - Based on OpenOffice - Compatible with Microsoft
This basically means that, citing from TLDRLegal’s quick summary:
You must make the source code for any of your changes available under MPL, but you can combine the MPL software with proprietary code, as long as you keep the MPL code in separate files.
which IMHO perfectly suits extensions.
Yes, you can. For any code that has been created by you and as long as you separate it from any other code (making an extension is a good way to do it), you are the one who determines its license and its distribution terms. So, good luck!
Here’s an example of non-free LibreOffice extension: http://www.orfo.ru/download/ (used to be a paid one, now free-of-charge, but still no free software).