I find that native speakers often use "had + meal" when they want to emphasize where/when/with whom you eat. For example: "I had lunch at Marco's and it was fantastic!" "I would love to try your cake but I'm not hungry, I just had dinner." "Would you like to stay and have breakfast with us?" Does that make sense?

In the united states, we say both "eating" bfast/lunch/dinner and "having." They are used interchangeably. Can't comment on what they say in the UK. We definitely don't say "take."

i usually say have breakfast / lunch / dinner. eat is common too. I think its just a preference take breakfast is understandable but not not really common

You can say either "have" or "eat". Breakfast, lunch and dinner all mean food... which you logically eat anyway... so "have" fits perfectly. The use of "take" is a little older, and I think most moderns speakers opt for "have". We still use "take" for medicine, of course.