Why is it lik here, then? From what you wrote it seems that som would be better if we want to say "I will rise like the Sun". I will rise identical the Sun doesn't make much sense, does it?
If you're saying it metaphorically it would be fine. But you can of course assume that 'I' in this case is also a planet.
Americans almost never use "shall". My understanding of British English is that "shall" is used to form future tense for first person (I/we), and "will" is used to form the future tense for second and third person (he/she/you/they). Then, to express commands, determination, or strong desire, you use "shall". So "You shall pay the rent" is a command or exhortation for you to do so, and "You will pay the rent" is a simple future tense statement of fact.
tldr; skal can mean both, depending on the meaning of "shall" or "will".
Confirmed. So saying, Brits almost never use "shall" either. Those that do are either being very formal, or their background was one that emphasised "correctness" as a matter of status.
Shall we dance? (1st person)
You shall go to the ball. (emphatic 2nd person)
Its popularity varies by region as well, regardless of status or formality.
"Shall I --?" can mean "Do you want me to --?"