I found that most chemical elements (ones I checked) are denoted by single character in Chinese. This is understandable for historical elements, but how it can be for new elements like Uranium and Plutonium? Does this means, that chinese people can invent new characters nowadays?
You're right. We did invent a bunch of characters for chemical elements in 20th century.
We made it just one character by combining different radical(偏旁) together, but people can associate them with the English words simply by their pronunciation.
You can read more about it from this Wiki article: Chemical elements in East Asian languages
Yes, we do invent new characters, but it's more common that the character was invented long ago and dead, and we just resurrect it to be the character of a chemical element. In the past, only the emperors had the right to invent characters. In Ming Dynasty, the first emperor made the rules that one of the comprising characters of an imperial kinsman's name must contain one of the "five elements"（“五行” 金 木 水 火 土）radicals In it. However, there weren't adequate elegant characters meeting the requirements. So they contrived many characters for this only purpose. These characters contribute to naming many chemical elements.