Yeah its one of the points of fermenting. Maybe even the point of fermentation.

"Fermentation was primarily developed for the stabilization of perishable agricultural produce."

https://www.sciencedirect.com/topics/food-science/food-ferme...

I've heard of Indian dry mango pickles that are ~20 years old! I guess a product that is dominantly colonised by harmless bacteria is unlikely to be taken over by nasty things, unless it sports food that is tasty to harmful organisms and not friendly ones. Maybe the best defence is the dominant bacterium having eaten all the available sugars so that little further fermentation can occur (and the bottle won't explode)

Yes! Fermentation of fresh foods with lactic acid bacteria increases the acidity of foods and hence the shelf life. As far as I know, though, you also have to add salt to suppress the growth of less desirable microorganisms.

Edit: You can skip the fermanation step by pickling your vegetables with a suitable vinegar. The taste will be much different though.

Fermentation does a few things - it removes some of the excess sugars so other microbes don't have much to feed one, it changes the ph of the liquid so that again it is inhospitable to other microbes, and the mild alcohols can also inhibit other growths.

Wines can taste great (better even!) after years of storage, I would have not problem eating a well ages fermented ketchup.