We are trying to create a table of standardised effects and standardised errors to compute for a meta-analysis. And I had a few questions around this

1. Can you get a standard error for pearson correlation, and if so can it be back calculated knowing the sample size, and r value. Or what other information do you need.

2. In a regression output I see people report unstandardised coefficients, standard error, and standardised coefficient. Is this standard error the standard error of the standardised coefficient or the unstandardised?

3. How do you back calculate a standardised error if you have a standardised coefficient, p value, and n?

Q1 The usual suggestion for meta-analysis of correlation coefficients is to transform them first. Although it is possible to calculate a standard error for the Pearson product moment statistic it is only really useful for very large sample sizes and population values of $$r$$ close to zero. The question linked to by @Glen_b in a comment Expected value and variance of sample correlation gives more details.
The usual transformation suggested first by Fisher is the hyperbolic arctangent $$z = \frac{1}{2} \log \left(\frac{1 + r}{1 - r}\right)$$ with standard error $$\frac{1}{\sqrt{N - 3}}$$ where $$N$$ is the sample size. Note this is strictly only correct for bivariate normals but it is widely used nonetheless. It does of course have the advantage of mapping from [-1,1] to [$$-\infty,\infty$$]
Q3 first back-calculate the value ot $$t$$ or $$z$$ corresponding to that $$p$$ and $$n$$. Then since you know that $$t$$ = coeff / se you can work out se.