I will pick the first misinterpretation: “The P value is the probability that the test hypothesis is true” (Greenland et al., 2016, p. 340). I will elaborate on it with an example of the coin example.
The coin is fair either P(H)=0.5 or P(T)=0.5 which is H0 (null hypothesis)
But if you believe that the coin is biased towards the head, getting more heads, then P(H) ≥ 0.5 which is H1 (alternative hypothesis)
Now, you experimented 100 times and got (observed) 60 heads of 100 times.
You calculate the p-value and get ~ 0.028 (2.8%).
Here, you cannot misinterpret 2.8% as the probability that the coin is fair or the probability of getting more than 60 heads.
Instead, the p-value indicates that there is a 2.8% chance of seeing 60+ heads by random chance under the assumption that the coin is fair.
Because the p-value will randomly vary with each experiment and each flip under the assumption that the coin is fair.
Reference:
Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. *European Journal of Epidemiology*, *31*(4), 337–350. https://doi.org/10.1007/s10654-016-0149-3
I might be wrong. Please feel free to correct me.