Are predictions of global warming, economic catastrophe and doom to be taken seriously or ignored? Can we expect G-d to take care of us no matter what? 

Numerous statements on this daf refer to the concept that G-d’s providence assures that every creature is sustained. This expresses a trust in the well-being of planet earth and its inhabitants which runs against the current political rhetoric. Yet, should we not be concerned?

The famous economist, Thomas Robert Malthus observed that an increase in a nation's food production improved the well-being of the population, but the improvement was temporary because it led to population growth, which in turn restored the original per capita production level. In other words, humans have a propensity to utilize abundance for population growth rather than for maintaining a high standard of living, a view that has become known as the "Malthusian Trap". (https://en.wikipedia.org/wiki/Thomas_Robert_Malthus )

Based on the theories of Malthus, economists Paul and Ann Erlich predicted a “Population Bomb”, which would supposedly have led to massive famine by the 1970s and 80s. However, this did not occur. Why?

Enter the opposing economic viewpoint of the Cornucopists who believe that the greatest single resource is human beings and their ingenuity. Therefore, they believe that an increase in population, while requiring greater resources will also produce the intellectual capital to discover and mine resources of the earth and the universe, to greater and greater degrees. This is why the science fiction movie trope that aliens, who have a sophisticated enough technology to travel with warships over thousands of lightyears, to invade Earth is absurd.  There is enough resources, minerals and even water on asteroids and other exoplanetary objects that there is no need to come to conquer Earth.  That is aside from the technologies that could harness energy more efficiently such as making a Dyson Sphere around and available star. Or, let us not even fry our brains with thinking about Ray Kurzweil’s looming Singularity, where all of human consciousness can be uploaded onto a computer chip.  You can have human experience and life lived on a “simulator microchip”, powered by micro-voltage that could easily run on solar power.  Yes, this is scary, but not impossible. 

On a more 21st Century practical level, while fossil fuels are now likely causing global warming and may eventually run out, they’ve also fueled the industrial and technological revolution that will eventually allow for carbon-free technologies such as nuclear fusion, which are only years away from being implemented. That is aside from more efficient ways to drill the remaining oil as well as ways to possibly repair the environment through nanotechnology and terraforming.  The bottom line is, arguably, humans make at least as many solutions as they do problems.

To prove the point that resources become more available and abundant over time instead scarce, a famous bet was made between two economists. In 1980, economist Julian Simmons made a bet with Paul Erhlich that the prices of five key commodities, adjusted for inflation, would be cheaper in 1990 than 1980. Indeed, Simmons won the bet, which in many respects proved his point, that technology allows for more access and discovery of greater resources despite, or even because of, the increase in population. It should be noted that this bet has been repeated and not always won, however the idea is certainly compelling.

https://rationalwiki.org/wiki/Cornucopian_vs._Malthusian_debate 

None of this however exempts us from using our hearts and minds to properly budget and manage our consumption and waste. There are several directives in the Torah indicate the value of conservation and stewardship of the planet earth, such as:

Bereishis 2:15

וַיִּקַּ֛ח יְהוָ֥ה אֱלֹהִ֖ים אֶת־הָֽאָדָ֑ם וַיַּנִּחֵ֣הוּ בְגַן־עֵ֔דֶן לְעָבְדָ֖הּ וּלְשָׁמְרָֽהּ׃

⁦The LORD God took the man and placed him in the garden of Eden, to till it and tend it.

Devarim 20:19

כִּֽי־תָצ֣וּר אֶל־עִיר֩ יָמִ֨ים רַבִּ֜ים לְֽהִלָּחֵ֧ם עָלֶ֣יהָ לְתָפְשָׂ֗הּ לֹֽא־תַשְׁחִ֤ית אֶת־עֵצָהּ֙ לִנְדֹּ֤חַ עָלָיו֙ גַּרְזֶ֔ן כִּ֚י מִמֶּ֣נּוּ תֹאכֵ֔ל וְאֹת֖וֹ לֹ֣א תִכְרֹ֑ת כִּ֤י הָֽאָדָם֙ עֵ֣ץ הַשָּׂדֶ֔ה לָבֹ֥א מִפָּנֶ֖יךָ בַּמָּצֽוֹר׃

⁦When in your war against a city you have to besiege it a long time in order to capture it, you must not destroy its trees, wielding the ax against them. You may eat of them, but you must not cut them down. Are trees of the field human to withdraw before you into the besieged city?

And see Ramban (Devarim 22:6) who describes a Torah prohibition against causing an entire species to be extinct.