RML provides a very consistent way to discover information about a solution

There are 4 types of models, objectives, people, systems and data.

The first models you should try to get are:

1) business objectives model /KPI model - what is the purpose of the system?

2) Org Chart / High level process flows - who are the key stakeholders and what do they do?

3) ecosystem map - what are the systems that make up the ecosystem and how do they relate?

4) Business data diagram - What are the business data objects and what is their relationship to each other?

Start out by trying to collect as much existing written information as possible, this could be in the form of training guides, technical documentation, existing process flows etc.

From there you can flesh out many more models.

Our book on RML goes much more into the details:

http://www.amazon.com/Visual-Software-Requirements-Practices-Microsoft/dp/0735667721/ref=sr_1_1?ie=UTF8&qid=1344872517&sr=8-1&keywords=visual+models+for

And a quickstart guide is here:

http://www.seilevel.com/wp-content/uploads/RML-Language-for-Modeling-Software-Requirements.pdf

 Sounds like you're looking at two new things: 1) managing a small team and 2) wanting to get on caught up on domain knowledge.

So, I do not have a list of "good questions" handy to help unearth that information, but having gone through a similiar situation recently, I do have a few suggestions.

First, I list out some of your favorite tools in your BA arsenal, and then list things you need to know about at your new domain in order to use those tools. Be starting with you do know and in your comfort zone, you can more easily identify and prioritize collecting the information.

Next, setup some workshops with related teams to get feedback on your understanding, but also use the time to broaden your question palette.

And last but not least, I'd suggest integrating domain research efforts with the new team setup... integrate working together through this identification process to help set up a good working foundation. They'll feel ownership of the process and you'll be buildlig valuable team trust.

Good luck & be sure to post a follow up of what you find!