1. Reading various anecdotes, seems like app developers need to update their apps to take advantage of the Pixel 4's new face unlock system. Not sure about the progress there, but I guess expect to be using passwords for some.
2. On Android, I just use the Gmail app and connect it to other services if needed. It's not a really great app tbh, but it works. It doesn't support push email on some services like iCloud, so that's a caveat. Other options include Outlook and Blue mail that I have used.
3. Due to the small batteries of the Pixel 4, don't expect much. You might need to opt for the XL version.
4. This is a big issue for me. I can never find an ideal podcast app on Android. Google's own app is junk. Some podcast apps that were great are old and still carry the holo UI from Android 3.0 era. I ended up using Podcast Republic, which is decent, but sometimes it has downloading issues. Your option seems better if you don't mind streaming your podcast. Apps like Spotify will do the trick.
Pixel camera is not "better" than the iPhone. It's just different. If you switched, you lose the wide angle lens, and one of the best video recording device.
If you really want to switch, consider Samsung. The Galaxy S20/S20+ are great phones, and they offer a much more complete experience than Google Pixel imo for similar premium pricing. If you're in the US, unfortunately the mid-range offerings are not too exciting compared to Asia.
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Agree that phones from the last few years, even budget ones, have been quite sufficient for normal uses.
As for the Galaxy A series, I would avoid anything below the A50 as the models lower than that uses the old and slow eMMC storage. A50 and up uses the faster UFS2.1. I have used Android phones with eMMC storage before, and boy do they slow down pretty quickly, especially when you're in the middle of updating or downloading files.