It would be better trying to write naturally and professionally. Sometimes even one link is enough and at other times when you are trying to explain things in details, using several links could be OK.
Using Links in your article is usually a good practice, you are providing a extra information. This helps a reader to understand the article. If your anchor text and the link provided are relevant then i think should be no problem to post your links in. please use proper keywords for anchor text and relevant link
I would recommend three links that have different landing pages and keywords.
I agree
About Article submission site it depends the guideline of each article site. Some article site can put 4 links in signature or resources. But mostly article sites can put 2 to 3 links in signature or resource per article.
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