* verb stem + 기 makes the verb to a noun just like 'gerund' in English.
** 밥 먹기 싫어요.
언니한테 얘기하기 싫어요. would be correct sentences.
*** verb stem + 기 is usually used with 좋아하다, 싫어하다, 바라다, 원하다 . For these verbs, an object marker 를 is commonly dropped. : -기(를) + 좋아하다, 싫어하다 etc.
**** verb stem + 기 (가) + 쉽다, 어렵다, 좋다, 싫다, 나쁘다,시작하다, 힘들다
***** "Yes". It is natural to use those sentences that you showed.