Yes - vitamin B12 isn’t found in plants. Other minerals are also harder to come by, like Zinc and Iron. The bio-available form of Omega-3 Fatty acids, EPA, DHA, and DPA are also only in animal products. Long-term veganism without health consequences isn’t possible without careful supplementation. If you eat fish and eggs, you are mostly covered, although I recall studies showing vegetarians had lower levels of B12 and other vitamins/minerals vs their omnivorous counterparts.

You can get all vitamins/minerals needed by just eating animal products, if you so desire. Plants don’t contain anything essential for human health, so far as we can tell today.

Worth noting that there are a wide variety of B12-fortified plant-based foods available (non-dairy milks, cereals, etc.). One can also find algae-based EPA + DHA supplements.

Yes, this is true, although I don’t believe these tend to be very healthy foods. Algal Omega3’s are a good source (although technically not a plant).

Collagen is really low for vegetarians which, I don't know about health consequences, but doing without it for long enough makes you look sickly.

This is not relevant to the question asked since it's about vegetarians who gave eggs and milk.

Given how many health vegetarian humans are our there, I'd say obviously not.

There are things that are harder to come by outside of meat. Iron is a big one I think, certain amino acids too I would guess.

Iron is available in plants. The question is mostly, what animals can produce by consuming plants that we need and we can't produce on our own.

No.

Source: my SO, who is a nutritionist with a master's degree on vegetarian diets