If there is too much content in a cell, how can I automatically split part of the content to next?

This free script might help you:

http://eugenyus.rudtp.ru/en/splitTRowByPars

Word is, in the end, a very different tool from InDesign. Things like very long tables with large, multipage cells are inherent and necessary in office documents, but must be manually managed and limited in a layout app. It's just a fact of the different usage — Word's a fairly lousy layout tool, and ID a mediocre text editor. 🙂

That feature is not in InDesign.

This has been a frequently requeted feature. You can vote for it in InDesign User Voice:

https://indesign.uservoice.com/forums/601021-adobe-indesign-feature-requests/suggestions/33854788-option-to-split-table-rows-across-pages