Welcome to Tropical Fish Keeping forum.
I would be fairly certain you have two quite distinct issues.
First the scum on the surface sounds like a common protein scum. This can form on the surface of any aquarium, though it seems more prevalent on some than others. It is not directly harmful but should be regularly siphoned off (I simply invert the water changer and siphon off the surface during the weekly water change) since it will reduce the gaseous exchange. A filter that has a gentle flow across the surface will usually keep this at bay. I used to use surface skimmers on my canisters and they handled this, but I stopped (very small fish and fry got sucked in) and I see it but usually only on one tank.
I say gentle flow because surface disturbance speeds up the gaseous exchange and CO2 is driven off before the plants can use it, which in a planted tank can be detrimental to the plants.
The other issue may be related to the temperature. For the fish you mention, it is not necessary to have the tank as warm as 81 or higher. A temperature around 77-78F would be adequate. Some of those fish can tolerate warmer temps long-term (rummynose), but others like the neon cannot. Neons should never be above 77-78F, and they would be very happy at 75F. The Bolivian Ram
the same, the corys also. Diamond Tetra
and Black Phantom Tetra
have ranges from 75-82 but there is no harm in maintaining them at the lower end. All of these (except for the neons) can be kept above 80F but should not be unless there are fish in the aquarium requiring that temperature (Discus
, Mikrogeophagus ramirezi
, some gourami, etc). You can check temperature ranges for fish in our profiles, click on the shaded name in posts or use the second tab from the left in the blue bar across the top.
Higher temperature means less dissolved oxygen in the water, and fish will naturally have to respirate more to obtain oxygen. With the plants you mention, provided they are photosynthesizing (the nitrate at zero says to me that they are), there should be no shortage of oxygen, but again, it will be naturally less with warmer temperatures. The slow growers may not make much of a difference, but swords (Echinodorus species) are high oxygenators and relatively fast growing though not comparable to many of the stem plants. But still sufficient for your setup.
Lowering the temperature may help the protein scum too; I have noted it is more prevalent on my warmer tank (SE Asian housing Chocolate and pygmy gourami) whereas it rarely if ever appears on the Amazonian tanks. Some think it also (like cyanobacteria) bears a relation to plants in the Cryptocoryne genus; I've no evidence either way, except I have crypts in that tank and not the others.
Kitten's suggestion on the filter is very relevant too. If the filter is slowing due to clogged media/pads, this can cause the fish to respirate more rapidly. I had this in my 115g Amazonian tank not long ago. I noticed one evening as I watched the fish that some of the corys seems to be breathing faster than normal, and they were just sitting on a log. Other fish were fine. So I started looking around the tank, and noticed the flow from the filter was less than normal, as the plants immediately in front were not moving at all, and usually they do slightly. I shut off the filter, opened it up, and saw it was obviously overdue for a cleaning, so I rinsed it out. Within an hour, the corys were back to normal. The reduced water flow meant they had to work a bit harder to get the oxygen they wanted. So that is worth remembering.
Hope this helps.