Hi. While I'm still a beginner with axolotls I happen to be an expert with outdoor pond plants. So I might be able to help you a bit with running plants in your pond.
1) Yes fish will "eat" your plants.
Gold fish are actually relatively plant friendly but if you run too many of too large a size in too small a space they will destroy everything. Less fish will be a good thing.
2) "Very Shallow"
While a pond being very shallow is a generally bad thing... how shallow is very shallow? The actual
deepest we recommend for planted outdoor ponds is only 50cm. And even down to just two or three cm there are plants you can grow. Presumably if you are running fish this thing is at least 15-20cm, that shouldn't be a problem it just may limit which plants you can grow and may alter the exact way you would pot them and grow them.
3) "Very Shady"
Many water plants including many of the more famous ones like water lillies actually do require a great deal of sunlight. However fortunately there are plenty of water plants and bog plants that will happily grow in partial or even full shade. People around here have been using Peace Lillies as a sort of shallow water emergent in aquariums, and that is no real surprise as a vast range of Arum lillies and Aroids thrive in similar conditions. In addition you could run some Rainbow Nardoo (which is a fern) some floating duck weed, some loose submerged Foxtail, and a wide range of reeds and other plants.
4) "Getting stuck in the pump"
Water movement sounds like it may be your very biggest problem. It isn't just bad for axolotls, it is bad for the majority of water plants.
With plants however it is easier to determine how much water movement is too much. As a general rule if water is falling onto plant leaves, or if waves are upsetting plant leaves (or as in your case sucking them into a filter/pump intake) then there is too much water movement.
The easiest solution is to simply turn off your pump. Alternatively you may want to resize whatever your running water feature or filter is to a more appropriate size for a small pond. Just be aware that for very small ponds there may not be room to seriously run a pump/water feature/filter
at all and still expect to run plants.
5) Axolotls in outdoor ponds
Guys around here can probably help you more. But I can give you this piece of optimistic news, and a small warning. I know for a fact that a man on Central Coast in NSW ran a great deal of axolotls in outdoor ponds under shade cloth for many years with great success (and almost no maintenance). But those ponds were of a pretty reasonable size and depth.
However I would be very careful of running axolotls in outdoor ponds (and despite having countless outdoor ponds to run them in will NEVER do so myself) because A) Kookaburras and other birds would pick off and eat axolotls in about 3 seconds flat (your flyscreen or whatever it is may help with this) and B) If the birds don't eat the axolotls then the axolotls will eat
everything else and I kinda like my diverse and large population of frogs.
Now I don't want to go around advertising my business on here overtly but I AM a proffessional horticulturalist who grows and sells plants specifically for outdoor ponds. And my business does operate in Australia. We don't just sell plants we do provide free information and advice about growing them. Currently the business is closed and I am in China, so I can't help you out too much. But if you have any further questions then you can contact me in about a week or so by various means including a direct visit to our nursery where you could actually SEE how we grow plants in a wide variety of outdoor pond conditions.
Our website is
Here