Vq1: It depends. For me, no. Why? I don't spend all my money on fake meat alternatives and plus I forage for shit like dandelions (lol) which saves money. It all depends on what you buy. If you eat a lot of whole foods such as fruits and vegetables it will be cheaper but if your diet mainly consists of vegetarian alternatives it won't.
Vq2: Just google seach veggie recipes and find one you think is good.
Vq3: Me lol jk. Actually I don't know but a lot of famous people are veg.
What is exactly is your reason for going veg?
Make sure your diet is varied. Do not rely entirely on fake meat products. Eat a lot of fresh, whole foods like greens, fruits, nuts, seeds. Don't go overboard on the dairy either. Lots of vegetarians go psycho on dairy and that is one reason many of them have anemia (Iron deficiency).
Drule, answer three is not completely true. Vitamin B12 is synthesized by bacteria. The reason it's mostly found in animal products is because the animals either have the bacteria in their gut (we do too but I read somewhere it is too low to be absorbed by our body) or when cows eat grass they will eat some of the dirt with it which has the bacteria in it. There are some foods out their like Spirulina, Wheatgrass...etc that claim to have naturally occuring b12 in them but I've heard people say they are just analogues and cannot be used by the body but then I've heard people say they do actually have b12. Vegetarians don't need to supplement b12 a lot though because most veggies eat a lot of dairy which has it. I'm 99% raw and I don't take a multivitamin, I do eat nutritional yeast on occasion though just to be on the safe side. I take spirulina and wheatgrass

Alternatively if you grow some of your own vegetables you can eat them without washing all the dirt off 100%.
Magic Negro, if my food is shitty what is not shitty food? How are greens shitty?