Correlation Question

#1
I have to do a correlation analysis for a paper and I don't have much experience in practical work.
My data looks like this:
lowess.PNG Unbenannt.PNG open.PNG
The two variables have a linear (but not monotonic?) correlation but I think it is not normally distributed (last picture) and I wanted to ask if I can still do a Spearman correlation with this distribution?
 
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