I ran the testnet software without any problems, but I have a question: what algorithm is currently used for the testnet? Is this already the "cuckoo cycle" proof of work that was mentioned in the whitepaper, or some other algorithm?

Yes, now it does. An hour ago it didn't. So they corrected it, I hope :-)

We are still in the first 24 hours of phase 1, I think, but currently the calculator converts new contributions as 1000 AE for 1 ETH. Also, the wallet shows the text "get 1000 AE for 1 ETH till 1d 18h 30m". How is this possible?

If phase one started at 13h05m UTC on April 3, then "the first 24 hours" should last until 13h05 UTC on April 4, I think.

If you meant that the bonus would end on 23h59m59s on April 3, you should have written "the first UTC day of phase 1", not "the first 24 hours of phase 1".

Someone asked for a Factom rich list?

https://factoid.live

Is this a mandatory upgrade? Since you call it a fork and not a "hard fork", I guess it's not mandatory, but I want to be sure.

The purpose of Factom is not to store information, it is proof of existence, and proof of integrity.

Don't forget that Factom will not be used to store data, but to store hashes of data. 1000 GB is a lot of hashes.