I would like to make this vegetarian. So any suggestions of what to use besides fish sauce? Also would like to add tofu instead of eggs. This dish is

Try a Southeast Asian variety of soy sauce called thin soy sauce. The owner of the Vietnamese restaurant in my old neighborhood, who made really good vegetarian bun, introduced this to me as a vegetarian fish sauce substitute years ago and it's been a staple in my pantry since then. It has a nice umami-rich flavor that's much lighter than that of dark soy sauce and I think is a good stand-in for fish sauce (which I do also eat). That restaurant owner handed me a bottle of Dragonfly/Kwong Hung Seng brand thin soy sauce, but I've also seen a version made by Healthy Boy which I haven't tried. Many Asian markets in the US will have one or the other, or you can order it online.

I think tofu is very good in bun. This type of dish is intended to accept lots of variation in toppings, as Bittman himself suggests in the notes, and is certainly true even of more traditional versions of this in Vietnam.

I agree that you could just add in soy sauce, but you will be missing some of the nuance of fish sauce. Cooks Illustrated came up with a really good substitute to use for fish sauce. In a saucepan, simmer 3 cups of water, ¼ ounce of dried sliced shiitake mushrooms, 3 tablespoons of salt, and 2 tablespoons of soy sauce over medium heat until reduced by half.
Strain, cool, and store in the fridge for up to three weeks.
There are commercially made vegetarian and vegan "fish sauce" substitutes out there. I'm not vegetarian or vegan, so I opted to make this version to help my daughter cook dinner for a vegan friend recovering from surgery. As far as adding in tofu in place of the egg, I see no reason why you couldn't. It's a garnish, really, and a source of protein. Tofu might be best if it was pan fried to give it a bit of chew factor, and it would be tasty in the salad. Recipes are not carved into stone, so you don't need to feel bound to follow them strictly. So long as you understand changes in ingredients will not result in exactly the same dish, it's your business.

You can just leave out the fish sauce. You might want to add a little soy sauce. I think tofu would be a bit heavy with fine rice noodles. The eggs are boiled and used more like a garnish, so they do not have to be substituted. Some thinly sliced shiitake might be nice.