Is cheese you are eating suitable for vegetarians?
No, not all cheese are actually vegetarian. Specially if you are staying out of India read this very carefully.
Have you heard what is “Rennet”? 
Rennet is main ingredient to make any kind of cheese. 
There are different types of rennet:

1. Animal rennet which comes from the stomach of newborn calves or lambs.2. Vegetable rennet which can be made from a variety of plant sources such as fig, thistle, safflower, and dried caper leaves. It can also be made from genetically modified soybeans.

So If you are vegetarian, then avoid any cheese with rennet, animal rennet, or enzymes (which typically means animal rennet, although not always, but there’s no easy way to know) listed in the ingredients. Vegetable rennet will be listed as such.

“Be Vegetarian Be Happy”
“Live and Let Live”

Do you know the cake /ice creams (eggless) you are eating is actually suitable for vegetarians?
No, Most of the bakers use GELATIN to decorate the cakes. And yes for ice creams this is the main ingredient to set it.
And this is strictly no no for vegetarians. 
Because-
“Gelatin is an animal by-product sourced from animal hooves, bones, cartilages, and other parts of abattoir meat leftovers.”
So next when you buy cakes /ice creams /dips or even yogurt do not forget to check the ingredients for gelatin apart than egg in the product.
“Be vegetarian be happy”
“Live and let Live”