As a native user, I'll try my best to explain these questions.
Question 1
「这太棒了!」/「这是太棒了!」/「这真是太棒了!」
Here should be a special grammar point in Chinese. On building a sentence to describe a none, especially to show surprise, we make something like [n + adj]. Mostly, it is unnecessary to insert a BE verb.
In the 1st and 3rd sentences, the structures are like this:
这太棒了!
=> 这 + 太棒 + 了
=> noun + adj + x
这真是太棒了!
=> 这 + 真是 + 太棒 + 了
=> noun + adv + adj + x
However, the 2nd one's looks like this:
这是太棒了!
=> 这 + 是 + 太棒 + 了
=> noun + beV + adj + x
Adding a be verb in a Chinese sentence is like raising the pitch of a BE verb in English. For example:
A: Give them your phone number, and you can get 2 trillion dollars? Don't you think it is too fantastic?
B: It is too fantastic.
... is the same as ...
A: 给他们你的手机号,你就能得到 2 亿? 你不觉得这太美好了吗?
B: 这 是 太美好了。
Question 2
「一把美丽的椅子。」/「一把红的椅子。」
Here may comes no grammar point, just a -few- lot of rules of usage.
When we don't use 的
- A suffix exists. Such as ……式、……风、……味、……用 (for adj)、 ……化 (for verb)
法式料理、英式甜点、复古风打扮、工业风设计、蒜味土司、食用金粉、自动化工厂
2. The adj is too short. Such as 酸、甜、苦、辣、咸 (flavours)、煎、煮、炒、炸、炖、卤 (ways to cook)、大、小、高、低 (level or scale)...
酸葡萄、烂番茄、小蛋糕、炸鸡翅、卤排骨、苦巧克力
3. The adj is a noun
起司汉堡、鲔鱼三明治、火腿蛋、芝麻蛋卷、天空蓝
4. The adj is widely used
精制糕点、疯狂科学家
5. We are using it as a term.
草莓风味蛋糕、细胞核、有性生殖、泻殖孔交配
6. A 之 or 的 has been there.
第四代的在日韩国人
...and so many more
When we use 的
- The adj is so long
渣男一般的行为、四处撒野的小兔崽子、中华民国人民的自尊心、裤子口袋的破洞
2. An adv exists before the adj. Such a 很、超、超级、世界无敌……
超酸的葡萄、超级苦的巧克力、很大的蛋糕
...and so many more
When we use 之 instead of 的
- On a formal document. But no too much, or the articles may look boring and unnatural.
- Showing off our literary attainments. That is, to make the word/article looks more poetry.
Basically, there are so many different conditions and situations. Even the rules above, which I tried hard to sort out, don't work everywhere. Talk more with your Chinese friend will be great for you to understand these.