Hi, Ricardo, I am pretty sure that this is a difficult stuff for you to distinguish. Actually, there are some differentiations between Chinese and English, just like this one. Firstly, "your teacher had said that 是 can only connect two nouns" , this is not correct. For example, “我是谁？” "Who am I?" ,there is only one noun behind "是". The explanation that your teacher give you has a flaw,.You can't really recognize "老师“ as a adj. and a n. ”老师“ is just a word. It does not mean: a teacher who is really old, it just mean: teacher. Secondly, for your next question, "playing chess is the most difficult" ---- "下棋是最难的” the most= 最, very =很. You can't say that "playing chess is the most very difficult. It's incorrect. My English is not very good. Hope my explanation can help.

it decide what sentence you are use: because 是 in different sentence the meaning is different: (1 表示解释或分类：他～工人。《阿Q正传》的作者～鲁迅。 (2 表示存在：满身～汗。 (3 表示承认所说的，再转入正意，含有“虽然”的意思：诗～好诗，就是太长了。 (4 表示适合：来的～时候。 (5 表示任何：凡～。～活儿他都肯干。 (6 用于问句：他～走了吗？ (7 加重语气，有“的确”、“实在”的意思：天气～冷。 (8 对，合理，与“非”相对：～非。他说的～。实事求～。 (9 认为对：～古非今。各行其～。深～其言。 (10表示应承或同意（单说一个“是”字）：～，我就去。 (11 这，此：～日。～可忍，孰不可忍。比比皆～。 (12 助词，把行为对象提前表示只这样做：惟你～问。惟利～图。 (13 姓。 ha ha it is what i seach from the internet if you can't understand you can ask me or use translator

难 = to be difficult It is an "adjectival verb". Did your teacher tell you that? Probably not. Most will tell you they are adjectives. Well, they're not. That's the difference, and that is why you don't need 是. 下棋是最难的。 难的 = a difficult thing, and is therefore a noun. As such it requires 是. But you forgot the 的. The 的 turns 难 into a noun.

I think 是 can connect noun and noun, also can connect noun and adj. But note here noun refers to real noun and pronoun, and before each noun you can have adj, eg, 我们是好朋友 （we are good friends）,这个决定是错的(this decision is wrong). It is right to me that 很is used to connect adj to a noun, actually here omits a verb in this case, eg, 下棋很难(playing chess is very difficult) or 下棋是很难的

There some usages of 是， 1. connects two nouns; 我是学生，他是老师。 2.connects a noun with a adjective or a phrase that can play the role as a adjective ; 树叶是绿色的; 泛函分析是最难的数学课之一;这本书是关于战争的。 3. to say something exists; 箱子里装的是苹果;他满身是汗 4.to admit something you think is suitable or reasonable; 他说的是; 实事求是 5.refers to "yes"; A :你是张三吗？B:是。 6.refers to anything ; 凡是书他都喜欢;是活儿他都乐意干。 I wrote it myself so I think there must be more usages. However, above are basic ones.