-No, climate scientists aren't random people, they are scientists with PhDs and multiple Master's degrees in their related climate-study fields.

-They spend their entire life studying climate change because that's what they chose to do around age 17-18 and are passionate about the topic. They then go on to get a Bachelor's Degree, a Master's Degree, a PhD, and then Post-Doctoral studies in climate change studies, as well as continued research in the field for decades afterwards.

-Generally, (If in the USA) the student has to fund their schooling themselves, through massive amounts of student loan debt, and if lucky, scholarships. Post-grads can receive funding from the government if they have a long enough resume and show promise and aptitude to continue studying in the field appropriately, but this isn't all-too common. They can receive funding from banks, from parents, from corporations, from a separate job, from their own pockets. They live in the real world just like you and me.

-If they come to the conclusion that humans didn't cause climate change, then their study & results / findings would be peer-reviewed by fellow scholars and academics the world-round. If other scientists and scholars found their results to be accurate and well-researched, with strong evidence for being definite, their findings would become well-credited and accepted as generally accurate. The opposite is true, unfortunately.

-If students / scholars / academics / scientists / doctors on climate change presented research that humans didn't cause climate change, and the evidence and results were peer-reviewed and studied by other professionals and found to be accurate, no, they would not lose their funding. Quite the opposite actually, they would probably get more funding. They would only lose their funding if they presented false evidence or lied, or altered documents, or did something else that goes against the merits of the scientific method.