Should I include web pages in the references

The general rule for such things is that if you use the work of others for things not commonly known, then you must cite them. So, yes, cite web pages as needed and quote, formally, from them also when needed. But cite them even if you paraphrase things.

You also probably need to do more than just include a list of references at the end of the paper. The reason for including a reference should be made clear, usually in the text itself. There are exceptions to this, but it is better to be clear about why you include a reference and to be specific about what you have used within any referenced article.

The form of the citation/reference is a bit less important than the fact of it and unless you are given some specific format, use examples from things you read. Use something similar to what is used in Wikipedia or a textbook if you have no better source.

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One note about citing web pages. Since such things can change without notice, the correct thing is to include the date at which you last read/used the web page. "Last accessed 29 Jan 2021" for example

From my experience:

Q1: Include it as a regular reference (like an article) and if you find a published paper then exchange it. At our department we followed this strategy and published also our papers with references to websites.

Also I personally do not like this strategy, it seems inevitable in some cases. Be careful to include only really meaningful websites which correspond to a specific topic or software package.

Q2: I would recommend to use Bibtex and follow the style in this question: https://tex.stackexchange.com/questions/3587/how-can-i-use-bibtex-to-cite-a-web-page