Pillar 2a Questions - Leaving Switzerland

I have some questions related to cashing out the 2nd pillar contributions due to leaving Switzerland.

1) What countries have a double taxation agreement with Switzerland that allow reclaiming the withholding tax levied from withdrawal of 2nd pillar savings?

2) My company’s pension fund provider will refund the extra-mandatory portion of my pension. Am I going to be taxed based on the date of my request for refund (I am likely still a resident of Switzerland by then) or the date when I am paid by the pension fund provider (I  likely may have already left by then)?

3) Are the rates of a capital withdrawal tax and withholding tax the same?

4) Do you have a list of the capital withdrawal tax and withholding tax rates per canton?

1. You can find a useful map with information for both the pillar 2 and the pillar 3a here:
https://www.swissinfo.ch/ger/wirtschaft/auslandschweizer_auswandern-und-pensionskasse--so-spart-man-dabei-steuern/43670970
It is possible that new DTAs have been created since the article was written, but I am not aware of any.
2. In your case, the Swiss withholding tax will be deducted because you are withdrawing your voluntary benefits on the basis of leaving the country. The Swiss capital withdrawal tax does not apply. You will have to show proof of tax residence in your new country in order to reclaim the Swiss withholding tax (assuming a relevant DTA exists).
3. The capital withdrawal tax rates can be different from the withholding tax rates. However, both vary between cantons.
4. I don't know where to find a list of capital withdrawal tax rates. Those are quite complicated because they are calculated differently in different cantons. But you can find good amount-based examples for all cantons here:
https://www.vermoegenszentrum.ch/finanzrechner-und-vergleiche/steuern-auf-kapitalbezuege-aus-der-2-saeule-oder-saeule-3a
Your withholding tax rate depends on how much money you are withdrawing. But the maximum possible tax rate gives you a good idea of which cantons have the lowest rates. The withholding tax is deducted by the canton in which the retirement foundation (pillar 3a) or vested benefits foundation (pillar 2) is domiciled. You can find a good comparison here:
https://finpension.ch/en/withholding-taxes-pensions/

Thank you so much for your very helpful reply! 
Re: number 2, am I correct that the withholding tax is based on where my pension fund provider is domiciled (rather than where I live)?

That is correct. The withholding tax is levied in the canton where the vested benefits foundation (pillar 2) or the retirement foundation (pillar 3a) is domiciled. Be aware that the foundation may be domiciled in a different canton to the bank, insurance, or asset manager which offers the service on the customer-facing side. For example, Finpension is headquartered in Lucerne, but its foundations are domiciled in Schwyz. Refer to the contract terms and conditions for the domiciles of the underlying foundations.