Hi and welcome to the forum
I would say they are both young males. One of which has a lot of red around the gills and face, which could be caused by poor water quality or something in the water that is irritating it.
Check the ammonia, nitrite, nitrate and pH levels in the tank and do a 75% water change and gravel clean the substrate any day there is an ammonia or nitrite reading above 0, or a nitrate reading above 20ppm.
Increase aeration/ surface turbulence to maximise the oxygen levels in the water.
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What are the tank dimensions (length x width x height)?
What is the GH (general hardness) and pH of your water supply. This information can usually be obtained from your water supply company's website or by telephoning them. If they can't help you, take a glass full of tap water to the local pet shop and get them to test it for you. Write the results down (in numbers) when they do the tests. And ask them what the results are in (eg: ppm, dGH, or something else).
If you have hard water with a GH above 200ppm, you should either avoid the Gold Panchax and B. imbellis, or mix the water with reverse osmosis or distilled water to reduce the GH to 150ppm or less.
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When you say imbelis, I assume you mean Betta imbellis?
If yes, why do you want a single female B. imbellis?
Betta imbellis are uncommon and worth breeding. If I had a choice of keeping Betta imbellis or Gold Panchax, I would get a group of B. imbellis and breed them in a single species tank.
If the tank is big enough, you could keep Gold Panchax with Betta imbellis but I would not do it in an aquarium that is less than 36 inches (3 foot) long. The male Panchax can get grumpy and might have a go at the much smaller B. imbellis.