Hi! The closest English meaning of みよう is "try to~." So, もう一度竹内さんを誘ってみよう means "try to ask Takeuchi once again." 2. みましょう means "Let's try to~." because み in みましょう is the same with み in みよう and ましょう means 'Let's' . いいでしょうか means "~ will(would) be good?" So, なんで行けばいいでしょうか means "What means of transportation will be good (to go to 文化劇場)?" That is, "How can we go?" 3. いいのですmeans "~ be good." いいin いいでしょうか and いいのですmeans "good" in English. I'm Korean, but I can speak Japanese. I hope it helps!

1. みよう is the volitional form of みる. ~~[動詞](で/て/して)+みる as in 誘ってみる normally translates to "try ~~ing." E.g.: 飲んでみる=try drinking. 食べてみる=try eating. 行ってみる=try visiting, 電話してみる=try calling, etc. ("try to~~" is normally translated as ~~しようとする in Japanese, it depends on the context though.) 2. みましょう in 誘ってみましょう is the polite form of みよう. 3. ～～すればいいのです is the polite form of ～～すればいいのだ, "You can just~~", "You only have to~ " or "All you have to do is~~". Here you can rephrase it as ～～すればいいです(よ), which is the polite form of すればいい. すれ is the katei-kei(仮定形) form of the verb する. ば is a conjunctive particle (接続助詞).