Sounds like hurricanes and floods did this.

Nope. If you read the study, you will see that data was collected in 1976 and '77, and then much later, in 2011, '12, and '13. Pretty far into the study, they actually do summarize the effects of hurricanes on frogs found by a previous study:

The temporal pattern of E. coqui abundances in Woolbright’s (29, 30) El Verde study area (SI Appendix, Fig. S3B) departs from the monotonic, negative trends found in the other E. coqui populations, and required a segmented regression consisting of three phases. In the first phase, E. coqui numbers had a significant negative trend followed by a rapid increase during phase 2 from 6 to 57 individuals between January and October 1990, most likely due to immigration from surrounding areas following Hurricane Hugo. In phase 3, the population resumed a steady decline at about the same rate as phase 1, until the census ended 6 y later. The rapid return to the preperturbation rate of decline suggests the ongoing influence of climate change on birth and death rates.

So although the frog population did take a hit from Hugo (1989), it bounced back due to an influx from nearby habitats. Especially for winged insects, the population of insects is likely to behave quite similarly. Regardless, these fluctuations are superimposed on top of a gradual decay in population for both frogs and insects.

How can they say 98%? Did they inspect 100% of the rainforest?

No, they use statistics. If you have several sampling points scattered throughout the jungle and use a methodology identical to what you used back in the 1970's, you're going to get a good idea of general trends. As is standard practice, the scientists included their error bars in Figure 2 (see above link again). The downward trend is far inside any experimental uncertainty.

Higher taxes and we still pollute the same amount or more than last year.

...

It is all one giant money grab.

First of all, "pollute" is too broad of a term. This is about CO2 emission levels. And the data shows that the U.S. has indeed been reducing its emissions. Now, I concede that it's damn near impossible to definitively prove that imposing additional regulations (that is what you mean by higher taxes, right?) is what's responsible for the recent reduction in annual CO2 emissions. But that's still something I'd assert as almost certainly true.

The free market is even trying to convince you that climate change is forreal. And if you know how incredibly asshole-ish most scientists are, you'd realize that the climate change hypothesis would have been delightfully torn apart by peer review several decades ago, but here we are.

Money's nice, just not as nice as a stable global ecosystem.