Is it possible to play on a mobile phone? No matter where I tap, my keyboard won’t pop up to allow me to enter the numbers.

If it helps with an answer I’m using an iPhone 6s with safari.

Also what is “notes mode” for? I selected it and nothing changed that I could tell.

can't answer the mobile question.

However, notes mode adds little numbers to the squares: In the example below the circled 3 is added as a regular number because I'm certain of it. The circled 2 is added in "notes mode" because there are two places it can go.

Sadly Subeku is known to be unfriendly to mobile users. :c

There's a small suggestion about it here under games and a general suggestion thread about improving Subeku and Balloon Sweeper here that's not out of date yet, if you feel like posting about it. Don't feel like you should, though! xD