I am not sure you understand the terms you are using here. there is no evidence in this graph that CO2 is acting as either forcing (almost certainly untrue in this instance) or feedback (possible, but since the fall and rise in CO2 levels are minor any feedback will be only very marginal)
The latter doesn't follow. Small changes can have significant feedback effects. As for a few tens ppm out of about 270 ppm being
minor, that's a judgement call. It certainly is in comparison to the change over the last 150 years or so, which is over 30%. This, of course, is because we've been digging out fossil fuels and burning them in major quantities over that period. The right-hand end of the graph tells the story.
What it does show is
a. CO2 levels across oceans and atmosphere do seem to be in tight equilibrium- an equilibrium that is dependent on temperature.
Evidence from one Antarctic lake tells us all that? I don't think so.
From the rather simplified link you gave we see this
Which again points out that there is a considerable flux between the two pools ...
There is indeed, but since there's no fractionation in the process it makes no difference.
... (since the rarer isotope of Carbon is made in the upper atmosphere by solar radiation).
Sorry, you've lost me there.
b. The LIA did exist, was global in its effect - where some posters here were saying it didn't exist, was in a different time frame or was only European based.
Since by LIA you mean the period 1600-1850 you may well be correct. Not everybody specifies such a precise time-frame.
c. The fall and rise in CO2 seems to align approximately with sunspot activity, which reinforces the hypothesis that sunspot activity gives a measure of solar activity and this solar activity can have marked and global influences on climate.
Since the change in solar output is minor it can surely only have a marginal effect.
irony
The only question is what is the mechanism by which this solar radiation affects the temperature. Is it purely by changes in solar irradiance or some other mechanism?
The question is still if there
is an effect other than the obvious one : more solar output means more energy input to Earth's surface. We've had the opportunity to directly observe a period with no sunspots, using the best tools yet available to mankind, and the reduction in solar output has proved to be very slight, on the order of a few tenths percent. Not enough to influence global temperatures without some amplifying factor.
Which would mostly be CO
2. Acting as a positive feedback.
There were a lot of volcanoes in that period to confuse the issue as well, with the same CO
2 feedback. None of which has anything to do with
current climate change, of course.