How can you tell if the chainrings need to be changed or not?
Just try them if you're not sure from appearance. Chainrings tend to wear more slowly than cassette sprockets (though it also depends on material and size), so replace the chain and cassette, stay seated and ride the bike with gradually increasing pedal pressure and listen and feel for any skipping. They'll be no urgency to replace them if there's no skipping. Perhaps later a mechanic (or the YACF massiv via a photo) will advise if there's any need at all.
I'm curious, if I was to replace the cassette with a slightly different range what would I need to do differently with the chain? Currently running 50-34 chainrings and 11-25 cassette. Was wondering about increasing the teeth on the cassette slightly. I think i need more than the 25 to help with loaded rides on hills, such as with trailers. Not sure I've got much room to do this with the short cage derailleur. Would I be able to increase the 25 without changing the derailleur? If so what are the likely options and what affect would it.have on the chain lengths/number of links needed?
Check the capacity and maximum sprocket specs for your particular model and year of derailleur (in manufacturer's instructions/website), add a pinch of salt if you dare*, and that's what you can have up to. Each extra pair of chain links tends to enable a few extra sprocket teeth. Start off with the chain longer than you think you need, join, test and shorten/repeat as necessary.
There are chain length calculators out there, but I prefer the trial and error or experience methods. Ensure the chain is long enough for big-big (largest rear sprocket + largest chainring) IF you want it to cope with accidental shifting into this gear that you'd normally avoid. It doesn't have to work nicely or look right in this combination, just work without breaking anything.
* Usually one to three teeth, sometimes more. Have the chain as short as practicably possible if pushing the specs, otherwise the chain length is not so critical as there's some leeway when you're within the official specs.