Will internal write/read go at 250/300 MB/sec? Will transfer using USB port go at 250/300 MB/sec? Will any android phone do either of these?
NO. It's capped at UHS-I
And despite Helpstar's comments, his own link shows this when the author is transferring from the SD card he is only getting 70MB/s, which is still pretty good for UHS-1.
Unfortunately the Note 8 (and Note 9) are limited to UHS-1 and 104MB/s speeds (minus overhead).
All Snapdragon 835 & 845 devices are limited to the "SD 3.0" spec (technically SDXC 3.01) which only includes support up to UHS-I.
The SD 855 introduced support for UHS-II found in the Note 10, but still crippled by Samsung.
Internal storage supports UFS 2.1 which caps out at 1200MB/s which is where you'll see it flex in Helpstar's link via the external SANDISK SSD.
I have a Samsung T5 (now also a T7) for external transfer (handiest for backups and 4K video transfers, and I could never get more than 83MB/s on an SD to SSD transfer on my Note 9 (with a 256GB Sandisk Extreme Pro [I didn't have bigger/faster cards until the N10+ ]).
Unfortunately the Note 8/9 also doesn't support low-latency App usages with A2 either (and Samsung crippled what A1 support there is), so a regular UHS-I / U3 / V30 / A1 is pretty much the cap for SD cards. (theoretically UHS-I V90 but not really)
https://www.qualcomm.com/products/snapdragon-835-mobile-platform
https://www.qualcomm.com/media/documents/files/snapdragon-835-mobile-platform-product-brief.pdf
(note the SD Storage / Memory sections in the Qualcomm 835 product pages)