Meats do contain protein and many individuals select meats on their protein diet. However, you can still be a vegetarian and select a protein diet. Eggs are rich in proteins and are an excellent selection for those on a protein diet.
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Vegetarians will have problems with calcium, iron, and protein intake if they are not careful. The Vegetarian Research Group explains this in detail on their site. They suggest eating specific foods like bagels, broccoli, rice, spinach, and certain nuts like almonds to assure they have enough protein in their diet.
Yes there are in fact some diet plans for vegetarians. They are special diets catered to vegetarians and there are some popular diets you can edit to work for a vegetarian.
They can be. A common error I see many vegetarians making is eating too many refined carbohydrates, too little protein and too few actual fruits and vegetables.
You can find all the information you need about low protein diets including recipes and sample menus online at www.everydiet.org/diet/low-protein-diets.
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High protein diets are favorable when trying to lose weight but maintain muscle. Some tips for high protein diets can be found here: http://www.beautips.info/fitness-and-diet-tips/follow-high-protein-diets-when-you-target-losing-weight-healthy/.
There are many whole grains which are a good protein for vegetarians. The queen of whole grains will be different for different people and their circumstances.
Iron and zinc.
Low protein diets can be important for people with diseased organs, such as Liver Failure. That is why sites such as 'www.everydiet.org' make available low protein diets and help you to find healthy low protein recipes.
Meat is not the only food with protein.