Spacing Guidelines for Modern Chinese Writing
No space is needed between characters.

A paragraph would start on a new line, usually with an indentation of two characters.

Space after punctuation is not required. The space you see is because the font tries to make punctuation to have the same width as a Chinese character.

In your first picture, the texts are article titles. There, to separate two phrases without using a punctuation, space is used. This usage usually do not appear in main article content.