Yes, Venus has large amounts of gaseous CO2, but is also has vast amounts of liquid and gaseous methane. Part of the reason Venus is so hot, is because each molecule of methane will retain approximately 40x the heat energy of every CO2 molecule. It also causes negative reinforcement feedback loops, with the interactions it has with solar radiation, oxygen, nitrogen and CO2.
Atmospheric methane is a sink for chlorine, but reacts with CO2 to create volatile and non-volatile organic compounds and with the nitrous oxide in the atmosphere to create ammonia compounds. The ammonia compounds then enter a feedback loop with the chlorine molecules where it creates hydrochloric acid, which tends to interact in non-pleasant ways with the O3 and H2O molecules that are also present.
As far as methane cycles go, there is no more such thing as a normal methane cycle for some of the reasons I've previously mentioned. It was known as far back as 1913 that the "natural" methane cycles would be toast because of ever increasing rice production, let alone in the current period, when we're adding in many metric tons of methane into the atmosphere directly as a byproduct of natural gas extraction. The Alaskan-Canadian-Siberian permafrost areas are also now releasing their stored methane (and CO2) into the atmosphere at ever increasing rates.
It's interesting to note that in the 25 years prior to 1993, rice production had increased 47%, and that the current estimates of production from 1993 onward to 2020, will increase by approximately 156%.
As far as timescales go, it's hard to tell, we've already done more damage in 200 years as a species than anyone could have possibly imagined. One of the earlier climate researchers (about 1989 or so) theorized that in those short 200 years, we had already pushed the human-habitable lifespan of the planet 3/4ths of the way to completion.