In the meeting, I want to ask him what were the tools & practices that
QA used at his previous company. The answer to this will
indicate/suggest if there could be any major technical & process
improvements here or not.
I don't want to catch the manager off guard & I also don't want to
sound too probing. What is the best way to get answers from him ?
Something like "Can you tell us a bit about the tools and practices you used at your previous company?" should work just fine. Whenever I've joined a company and taken over an existing QA Department, I've usually held just that sort of introductory meeting and volunteered just that sort of information.
That said, I disagree with the premise in "The answer to this will indicate/suggest if there could be any major technical & process improvements here or not.".
A QA Manager can only work within the context of the company/department/budget given to them. While I have general philosophies of how QA should work, it never comes out exactly the same twice. Often, the needs of the new company don't match the needs of the prior company.
I've worked for some companies that desperately needed everything, but had little budget. I had to focus on the near-term while trying to set the stage for the longer term. I've worked for other companies where the near-term was already under control, and that had enough budget to work on higher-level achievements.
And I've worked for other companies where I was told what my priorities were by upper management - and where they weren't at all like the prior company, nor what I would have chosen myself.
Instead of asking just about the previous company, consider asking "And what are your priorities coming into our shop? Where do you want to see us go?" I think you'll get more meaningful answers.