Do plecos NEED an air pump?
Plecos and bettas can be together, but only in a larger tank, starting at 20-30 gallon for the smaller "plecos". You might like nerite snails, they're far better algae eaters. Could I convince you to get a small sponge filter or Azoo Palm filter and some nerites instead of a pleco?
Your betta needs a filter, Any type of filter can be easilly diffused to reduce the current, and other filters dont need to be diffused. Their is no way that too much oxygen can get into water, Even if it did, Betas are labrynth fish, and they get oxygen straight from the air when they come to the water surface. Meaning that they probobly get more oxygen then the non labrynth fish species. Bettas will attck other bettas, and fish that they mistake for other bettas. But in a large enough tank, many bettas will live fine, even benifit from a wide variety of tank mates. The bettas fins are vulnerable to nippy fish, and active fish, bettas are easill out competed for food, especiall when they are still getting use to life with tank mates, so tank mates must be carefully chosen. A plco could live with a betta, but the smallest dwarf betta nedds a 20 gallon tank, and more commonly avalable dwarf pleco, like the bristlenose need at least 30 gallons or more. And other pleco species can get over 2 feet long. In the 5 gallon filtered and heated tank you could keep a snail or 2 with the betta. Few fish really need an air pump. The water can only hold so much oxygine at once, an air pump can help if you need more then average oxygenation, like if you turn up the temp to medicate, or in an overstocked tank. ALL FISH NEED A FILTER!
I've also researched about fish keeping, and nothing in your question agrees with anything I know about aquariums and aquarium care. I would suggest that you may want to research further.