I recently received the following questions from an African activist on capitalism, carbon, and climate, which I try to answer below:
1. Capitalism and Climate, how are these impacting us?
Capitalism is an economic system based on the private ownership of the means of production and their operation for profit. 
This means it operates by appropriating resources, transforming them, and selling them for profit, ie receiving more resources (money) than giving back. This creates a conveyor belt that transports resources (and degraded ressources, ie waste) through human society in particular and the biosphere following the principle of ressource extraction. Here, stronger, richer, and more powerful people are on the receiving end of resources and weaker, poorer, and powerless people receiving end of degraded resources, generally speaking.
While this leads to multiple social, ecological, and economic consequences creating injustice, the fact that our economic system is primarily driven by fossil fuels which provide energy and create pollution (especially carbon dioxide) and carbon dioxide is a greenhouse gase, is the reason that the harmful consequences of capitalism are most visible in the consequences for the climate. It is an example of externalizing the costs for damages (ie a deregulated climate) to future generations or poorer nations, which cannot defend themselves.
2. Colonialism and climate, can we put blame on colonialists?
Colonialism is a practice or policy of control by one people or power over other people or areas, often by establishing colonies and generally with the aim of economic dominance. 
Colonialism can be seen as a political and economic system, which shares the principle of resource extraction with capitalism. While colonialism as political system does no longer exist on the same historical scale, it shaped the current global economic system, which still extracts ressources from poorer and weaker countries to richer and stronger countries. According to Jason Hickel, even after taking developmental aid into account, richer countries (“Global North”) extract 10x as many resources from poorer countries (“Global South”) than vice versa .
Historically, nations which colonized other countries and are the beneficiaries of the current global economic system, are also nations which started industrialization early resulting in major responsibilities for the historic, cumulative carbon in the atmosphere which is deregulating the climate .
As of 2015, the USA was responsible for 40% of excess global CO2 emissions. The European Union (EU-28) was responsible for 29%. The G8 nations (the USA, EU-28, Russia, Japan, and Canada) were together responsible for 85%. 
In summary, colonizing nations (ie early industrialized countries, esp USA) take the main responsibility for the climate crisis.
PS: From the perspective of the Global South, it would be very important to stop exporting their ressources to the Global North, to save the Global North from its overconsumption. The Global North will not be able to stop its overconsumption (ressource addiction) on its own.
 Hickel, J. (2020). Quantifying national responsibility for climate breakdown: an equality-based attribution approach for carbon dioxide emissions in excess of the planetary boundary. The Lancet Planetary Health, Volume 4, Issue 9, e399 – e40.
3) Paris Agreement: What we can do to achieve it ? What leaders need to take responsibility to fulfill their promises?
Nation states ratified the Paris Climate Agreement and, therefore, it is their responsibility to take climate action accordingly. However, for various reasons (eg profit lobbyism, fossil fuel industry, misinformation in mass media), the governments do not act accordingly or actively block climate action.
We, normal people, can make individual contributions by lifestyle changes (eg no meat, no cars, no flights), vote political parties who follow the Paris Climate Agreement, and last not least perform civil resistance in line with the methods outlined by Gene Sharp , and actively applied by groups like Extinction Rebellion (eg road blocks) or Fridays for Future (eg school strikes, mass protests).
Governments have to take a wide range of decisions to reduce the emissions of greenhouse gases of which the following seem most important :
- removing fossil-fuel subsidies and incentivizing decentralized energy generation (STE1, energy production and storage systems),
- building carbon-neutral cities (STE2, human settlements),
- divesting from assets linked to fossil fuels (STE3, financial markets),
- revealing the moral implications of fossil fuels (STE4, norms and value systems),
- strengthening climate education and engagement (STE5, education system), and
- disclosing information on greenhouse gas emissions (STE6, information feedbacks).
4) Climate budget: How it is important and what we can do to minimise it so that it fits our plans?
The mass of carbon in the atmosphere directly correlates with the increase in global surface temperature (cf Transient Climat Response to Cumulative Emissions (TCRE) equation, for discussion see . The carbon budget corresponds to a certain amount of carbon humanity can emit while probably limiting global warming to a certain threshold (eg. 2 degrees Celsius global warming compared to pre-industrial level).
Possible actions to stay within the carbon budget are described above (see point 3). At present (2021), a massive transformation of the economic systems on national and international level similar to the mobilisation during World War II is needed to reduce greenhouse gas emissions by 45% until 2030 to limit global warming to 1.5 degrees Celsius . However, some scientists argue that is estimate is too conservative and limiting global warming to 2 degrees is what the best human efforts still may achieve .
 Steffen, Will (2019).The Big U-Turn Ahead: Calling Australia to Action on Climate Change. https://www.youtube.com/watch?v=OzQsjuzr3_M
5) What solutions do you have to tackle this Climate Crisis?
I recommend personal lifestyle adjustments (eg no meat, no cars, no flights), voting, and civil resistance to create political and social pressure on all levels. After all, the climate crisis is not a natural crisis (eg like an earth quake), but a psycho-social-political crisis, because it is human decisions which make us dig holes in the ground and burn the stuff we find.
6) According to IPCC report what can we do? What next?
Accorging to the IPCC report, greenhouse gas emissions have to be reduced by 45% untill 2030 and completely stopped between 2040 and 2050 to avoid irreversible, dangerous global warming which will severely damage human civilisation (rough summary from memory, see  for details).
Required climate action by individuals, and governments was discussed above.
Next steps required are increase the political and social pressure on people, corporations, media, and governments to follow the Paris Climate Agreement using all possible methods, especially civil resistance (non-violent direct action) .