It's possible to get everything you need from a strictly vegetarian diet - but it's very, very difficult.
No it's not. It really isn't. If what you say was true we would see vegans and vegetarians having poor health on average. In reality vegetarians have slightly better health than meat eaters in most studies, mostly because they're frequently the types of people who don't smoke and drink. When lifestyle habbits are taken into consideration the difference in health between vegetarians and meat eaters is slim to none.
Seriously, every now and then somebody comes up with som study to push the benefits of a particular diet. Vegetarian, HIgh carb, low carb, fish based, low GI, omega-3, but these always fail to live up to the very simpel scrutiny which shows that as long as you eat a varied diet, get the vitamins you need, and don't poison yourself with huge quantities of junkfood/drugs, you're going to be reasonably fine.
As for how to get all your vitamins and amino acids on a vegan diet. Vary your source of protein, take a B12 supplement, and eat 3 meals a day. You really don't have to worry much more than that.