The odds of an Ava "death stem" snapping are probably overstated. But on the other hand, if it does break, you're going to suddenly lose control of the bike and you're probably going to crash. Personally, even though I thought the risk was pretty small, I replaced the stem on my own Peugeot UO-8. But I also did it to accommodate a wider handlebar since the stock bar was uncomfortably narrow.

I can see from your pics that your front derailleur's cracked. No surprise there! SunTour made a couple of derailleurs that use similar cable routing. A SunTour Spirt or Compe-V can typically be found for $10 or so on eBay, often still in its original packaging, and would be a plug-and-play replacement. A rear SunTour derailleur from the same period also makes an excellent replacement for the Simplex rear, if necessary. Just because your rear isn't shifting right doesn't mean your derailleur's broken, so you may want to troubleshoot before replacing it. (On the other hand, a decent replacement is bound to be more reliable, so it's your call.)

If you're curious to pin down the date of your bike as closely as possible, you'll probably find date codes on a few components. On the backside of the rear derailleur's cage, right between the two pulleys, you'll probably find a stamp with the month and year the derailleur was made. You may also find date stamps on the rims and hubs.