Image below from article is 7dpi and 412x324. After reading mentioned article I got understanding that DPI is for printing and pixels is for display. So if I not expect images from web page to be printed I should use lowest DPI, since higher DPI takes more space. I'm right?
There are 3 images. One is at 7 other is at 700. It does NOT matter.
PPI is a little metadata text that electronic mediums, (aka webpage, video) do not use.
Space has nothing to do with it. If you refer to the dimensions, a bigger picture occupies more space than a small one.
If you refer to "weight" or disk space it depends on the compression of the image and the information that the image has. A forest picture has more data than a flat blank white wall's picture, so the second one can compress better.
This is really just a duplicate of all the other ppi/dpi tagged questions IMO.
However, the answer to your final question is:
DPI (actually PPI in digital images) is stored as a single number in the header of the file. When a file format actually supports it (I don't think PNG stores PPI), it is most likely only about 1 or 2 byte(s). So the PPI value has virtually no effect on the file size.
For a normal photo, the uncompressed file size is determined almost exclusively by the number of pixels multiplied by the number of color channels (3 for RGB; 4 for CMYK; add one for alpha channel). So RGB images are usually (width-px * height-px * 3) bytes large.
Two things to note however:
When creating documents, final rendering of typefaces and effects can potentially be affected by the document PPI setting.
Some software (usually for-print-oriented software) will prioritize PPI or assume low PPI if it has the flag. This is why placing images in some software makes them appear gigantic.