Hello Grzegorz_S,
Thanks for asking the Apple Support Communities for help with checking spelling in Pages.
I recommend going through the info and troubleshooting in this help article: Set up auto-correction and add words to your spelling dictionary in Pages, Numbers, and Keynote - Apple Support
Please start at the top to ensure everything is setup correctly on your Mac, but then there are two sections I believe may help your situation.
1. Use auto-correction with other languages:
"Auto-correction is available for languages that your Mac is set up to spell check. To see these languages, go to System Preferences > Keyboard > Text and click the Spelling pop-up menu. Click "Set Up" to learn how to add spelling dictionaries for additional languages. On iPhone or iPad, auto-correction is not available for all languages. "
2. For words the dictionary is not sure of, it underlines. You can check the spelling and add words to the spelling dictionary:
"When Pages, Numbers, or Keynote detects a word it doesn’t recognize, it underlines the word with a dotted red line. You can add the word to the dictionary on your device used by iWork and other apps so that it recognizes the word and includes it in spell check:
- On Mac, Control-click the word, then choose Learn Spelling."
Thanks and have a wonderful day.