I am glad you're willing to educate yourself. I hope to give you at least a starting point and will try to address the points you made.
1) Regarding the correlations: The reason why you don't "see" the correlation (i.e. the lines don't perfectly overlap) if you plot CO2 and average global temperature is because there are other effects that obscure the correlation. For example, on the scales of 500 million years, the power coming from the sun (solar luminosity) has increased [1]. Milankovitch cycles are also important over longer timescales. Albedo changes of Earth's surface, etc. I have already cited the principle control knob paper. If you don't agree with the results, we can discuss that but, if so, please give some arguments instead of "I don't believe it".
2) "CO2 lags temperature": this is true in some cases. Vostok ice core is often cited and indeed the authors point to a ~1000 year difference between CO2 and temperature [2]. A more recent analysis [3] goes into more detail on a global sample. They find that on average, CO2 leads temperature but in the southern hemisphere, temperature leads CO2. This lag can be explained by ocean circulation changes.
3) "multiple periods of warming and cooling in the last 1000 years, that were just as bad or worse as what we're in now": A landmark paper was released this year reconstructing the global temperatures in the last 2000 years [4] and they concluded the current warming is global and warmer than ever. Other warm periods in the last 2000 years were simply a) not as warm AND/OR b) not global. One image says it all [5].
4) Record cold not reported? I get a lot of search results from mainstream outlets when searching [6]. Of course, one cold/warm year does not disprove/prove global warming, but you know that. Also, weather and climate are different but you also know that. Popsci did an article explaining how this cold can be interpreted [7].
[1] For a short explanation, see Wikipedia: https://en.wikipedia.org/wiki/Solar_luminosity
[2] "CO2‐climate relationship as deduced from the Vostok ice core: a re‐examination based on new measurements and on a re‐evaluation of the air dating", https://onlinelibrary.wiley.com/doi/abs/10.1034/j.1600-0889....
[3] "Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation", https://www.nature.com/articles/nature10915
[4] "No evidence for globally coherent warm and cold periods over the preindustrial Common Era", https://www.nature.com/articles/s41586-019-1401-2"
[5] Image from [4] https://media.springernature.com/full/springer-static/image/...
[6] https://duckduckgo.com/?q=record+cold+2019
[7] https://www.popsci.com/cold-weather-climate-change/