Translation:Is this question easy?
Yes. It's usually used to refer to test problems or test "questions", which is why it's been translated that way. It can refer to other types of problems though
Because as another user stated above, 問題 (もんだい) is used for problems in a test or a textbook.
Is the difference between かんたん and やさしい that かんたん typically describes nouns and やさしい verbs?
かんたん can be easy but also simple. やさしい is easy but when you use it to describe a person it can mean kind. Both can be used to describe nouns.
To make い-adjectives into adverbs drop the い and add く, e.g. やさしく. For な-adjectives add a に, e.g. かんたんに.
Warning: yasashii/易しい (easy) is NOT the same word as yasashii/優しい(nice) !!! They are just homonyms.
かんたん and やさしい are both adjectives, so they both describe nouns or pronouns. They both mean "easy" or "simple" and are interchangeable most of the time with little or no loss in meaning. The difference is that かんたん is for things that are objectively easy (e.g. a simple task) and やさしい is used for things that are easy in the speaker's opinion (e.g. an easy exam).
From these comments it seems like もんだい is more like a test question (problem) than a question you'd ask. What is the word to use when you have a question, then?
I wouldn't use 持って here because it means "hold" or have something physical. ある alone is enough for questions.
I answered "Was this problem easy?" And was marked incorrect. Was my answer wrong? I thought もんだい meant test problem/question.