be+going to,will,verb+S未現式問題

1. 你老師沒有說錯, going to + verb可表達一個未來的arrangement (安排) 或schedule (行程), plan亦是安排之一種, 所以可以用 present continuous tense去表達, 舉些例句給你
I am going to get accomodation in Palace Hotel during my business trip to USA (下榻Palace Hotel是一個安排, 所以用going to +)
May is going to visit Japan next month (一個計劃)
The train is going to arrive at 14:20 (一個行程)

至於will是表示一個possibly happen event in the future
The weather foreast informs that it will rain tomorrow (天氣預告是一個預測, 所以可能下雨, 亦可能不下)
If I achieve a distinction at Mathematics in next examination, father will buy me an i-Pod for my gift (1st type conditional sentence, 即發生第一種情況便可能發生第二種情形, 另外有zero type, 2nd type & 3rd type conditional sentence, 想知詳情可去http://netgrammar.altec.org/Units/Unit_15/a101c15_201000.html看看)

2. 你沒有搞清楚, 顧名思義present tense就是現在發生之事情, 而present contiuous tense就是現在正在發生之事情, 而不是一個指定的時間(a certain point of time可以是現在, 過去或將來)或者你覺得我這答案很無聊, 但事實就是如此, 我也不明你為何問這問題