When can I expect my refund from the new unemployment law and will I get an amended return ?

I don't think you will get a corrected tax return.

If you have filed early before the exclusion, the IRS will recalculate your return for the new 10,200 unemployment exemption for you. There is no need for taxpayers to file an amended return unless the calculations make the taxpayer newly eligible for additional federal credits and deductions not already included on the original tax return.

Just keep waiting.  The IRS is sending them out in batches over the summer.

See IRS article May 14, 2021

https://www.irs.gov/newsroom/irs-begins-correcting-tax-returns-for-unemployment-compensation-income-exclusion-periodic-payments-to-be-made-may-through-summer

And see,

https://www.irs.gov/newsroom/irs-sending-more-than-2-point-8-million-refunds-to-those-who-already-paid-taxes-on-2020-unemployment-compensation

Do you need to amend your state return?

https://ttlc.intuit.com/community/state-taxes/help/do-i-need-to-amend-my-state-return/00/2134732

You will get a letter explaining the additional refund. You will not get an amended return or a corrected tax return. You won't get the letter until about a month after you get the refund.