It is used to make offers and suggestions and to ask for advice. What time shall we meet? Shall we vote on it now? What dress shall I wear? Shall I open the window?

in polite requests like "Shall I open the window?"

Don't use it. Here in America, I never hear it in everyday conversation. We say "will" instead.

Yes, learn to use "shall", especially if you want to be a good speaker. It does have specific uses and is still in common use. You can try to ignore it, but avoiding it will only show your English skills are limited.

In speech, the usual rule given for the use of shall and will is that where the meaning is one of simple futurity, shall is used for the first person of the verb and will for the second and third: "I shall go tomorrow;" "they will be there now." Where the meaning involves command, obligation, or determination, the positions are reversed: "it shall be done;" "I will definitely go." However, shall has come to be largely neglected in favor of will, which has become the commonest form of the future in all three persons. "Shall" retains it's traditional meaning in the written word, especially in legal, technical, or military contexts.