Does a potential IPO indicate that the corporation's financials need some help?
Not really. An IPO would be regulated by the market regulator's stringent condition. If anything, it is a sign that the company is in good financial health at the moment, as otherwise, why would a public investor invest money in it.
Do companies typically fire large numbers of employees when undergoing an IPO?
Usually no, because fixed cost optimization by rationalizing the workforce is a negative signal to the market. Basically, if a business needs eliminating positions for getting healthy in the 1 year run up to the IPO, it would signal something is not right with the fundamental business model.
would the company's software, assets, & data change a lot after an IPO?
You can expect the company to have more regulatory compliances to follow once it goes public, because now it is under public scrutiny, and any avoidable negative news is bad for the stock price. But other than that, changes will always be there, however, they are hard to quantify.
This gets me nervous because I would think it's a bad idea to join a company so soon before an IPO. Is this a valid concern?
It isn't really a bad idea for the reasons you've mentioned.
However, know that some employees who have worked (hard) for years there might be holding more stock options, which would have appreciated significantly by the time of IPO. Them earning (deservedly) more money can be unsettling for some people.