What are these flying bugs in my white tree frog's tank? Are they harmful?

By your description, it could be a species of isopod. These are typically not dangerous to tank inhabitants. The best option is to empty the tank and sanitize it. Use completely new substrate and monitor humidity levels. Keep the tank clean of stool and remove any uneaten food or dead/drying plants to prevent attraction of pests.

They are probably springtails. It is likely they came in on the plants or wood. They aren't harmful, but can be unsightly in large numbers. In bioactive tanks, they are used as "janitors" to clean up decaying matter, uneaten food and feces.

Remove her from her main tank and put her in a smaller hospital tank. You can use paper towels for substrate. Change them daily. Increase tank temps to 80 F with a basking spot of about 85 F. Maintain humidity at 70%. Mist her daily and provide a water bowl. Use only dechlorinated water. It she isn't defecating normally, a soak in a honey and water solution may stimulate defecation. A dilute unflavored PediaLyte solution can treat or prevent mild dehydration. Offer appropriately sized prey, no bigger than the space between her eyes. You can also feed bits of nightcrawlers. If the redness and symptoms persist, have her examined by your veterinarian or a vet experienced in treating reptiles and amphibians.

It almost looks like a bit of substrate stuck to the belly. It could be normal pigmentation developing. Keep an eye on both spots. Monitor for rapid change or growth, lethargy, loss of appetite, redness or spread. Keep the enclosure clean and at proper temps and humidity. Hoppers looks good in the images otherwise(no redness, not skinny, not dry).

Without a close up image, it is difficult to determine what these dots are. They could be springtail mites. These are harmless mites that feed on decaying matter. High humidity levels and a food source draw them in. They may have hitched a ride in on the live food or new fat tails you acquired. Treatment involves removing food sources, decreasing humidity and sanitizing cages, bowls, etc. Soaking your affected geckos in water may clean them off.

It could be an infection. Being a new pet, it should be examined by your veterinarian or an experienced herp veterinarian to confirm good health or to diagnose and treat any pre existing conditions. Quarantine it for now in case the underlying cause is contagious.

It looks like a Gray Tree Frog (Hyla versicolor) in the attached images. Care is quite simple for this frog. They are very hardy, tolerating a wide range of temperatures and humidity. IF they hibernate, simply provide a moist substrate (typically a coconut fiber and soil mixture) for them to burrow. If they are active, offer crickets every few days. Mist the tank to maintain humidity and provide a water bowl. Here's a care sheet for you! http://www.reptilesmagazine.com/Frog-Amphibian-Species/Gray-Treefrog/