Hi Rich, and welcome to Tropical Fish Keeping forum.
One does have to be cautious with increasing oxygen in a planted tank, and with the oxygen increases comes a CO2 (carbon dioxide) depletion. Both of these are detrimental to plants.
Carbon is a macro-nutrient of plants, and while there is a fair bit of CO2 occurring naturally in a healthy tank from the fish and even more from the bacteria in the substrate particularly, the more plants the more CO2 is required and we don't want to drive it out of the tank. Assimilation of CO2 from the water by aquatic plants takes about four times as long as terrestrial plants assimilating the same amount of CO2 from the air, another reason to work to retain CO2 in the water. Water movement and surface disturbance speeds up the gaseous exchange (oxygen enters the water, CO2 is dispelled) so it is generally considered better to keep water flow minimal (sufficient for the fish's needs and the plants) and reduce surface disturbance.
If the air pumps (presumably with air stones in the water) are not part of the filtration system, I would definitely suggest removing them. They will serve no real purpose [your aquarium does not seem to be overstocked, and you have live plants--more on this momentarily] and may actually be detrimental. First, oxygen binds with several nutrients such as iron, making them too large for the plants to assimilate--result is a nutrient deficiency and adding more nutrients will not resolve this due to the oxygen. Second, the reduction in CO2 may be sufficient to cause a carbon deficiency sooner, affecting plant growth and increasing algae. If the water movement is too fast, the plants have even more difficulty assimilating nutrients.
Live plants produce a considerable amount of oxygen during photosynthesis. They can only photosynthesize if there is sufficient light (intensity and duration) and adequate levels of all necessary nutrients (some 17 of them). If light and nutrients are in balance, and the fish load is in balance with the water volume, and the fish are compatible [this reduces stress], there will be no oxygen/carbon dioxide issues. During the day there will be an excess of oxygen but not sufficient to be troublesome; and at night when many worry about CO2 increasing, there will not be an issue unless the tank is way overstocked or if CO2 diffusion is being added and continued during the night.
As for the number of plants, we speak of the tank being "well planted." This depends upon the plants and the fish. You can have a look at the photos of my 6 aquaria which are all well planted [photos are under the "Aquariums" tab below my name over at the left]. A 260 litre equates to a 70 US gallon [I think better in imperial measures
], and one of my tanks is a 70g. Plants will grow in to the aquarium over a few months, so this should be remembered when purchasing them. In my largest tank, the 115g, I have about 140 fish and I have never had oxygen/CO2 issues at night. If you could indicate the plants you have (species), I might be able to offer more.