Thanks did not understand any of that. Sorry.
No need to re-index if there are no problems.
You can check activity by looking for mds, mdimport, mdworker processes.
Clarifying...those two statements directly respond to your questions.
"Check [for] activity" means that seeing one/two/all(?) of those processes active in /Applications/Utilities/Activity Monitor indicates that Spotlight is doing its thing, but there's no guarantee
that you'll see any
of them active at any particular time. (I don't think you'll ever see "Spotlight" listed in AM.)