Congratulations.
It is safe to eat the first egg. It is not likely to contain anything bad. I make a habit of always cracking an egg into a separate cup before I add it to anything else so I can look at it and assure it is all right. On a very rare occasion you can find something that makes you think you may not want to eat that egg. This can happen with either a farm-fresh egg or a store-bought egg. Three or four tiimes in fifty years for me, so not very often.
There could be a couple of reasons the egg is small. Most hens lay small eggs when they start laying. The eggs will get larger as she lays, especially after the first molt. The young hen's egg factory is just figuring out what to do. Sometimes it makes mistakes, like laying an egg without a yolk. Sometimes the egg shell is soft. Most hens get it pretty close to right the first time and practically all that have problems straighten out within a couple of weeks. Some breeds also lay smaller eggs.
As far as feed, you need to be providing layer feed. It contains what they need to produce eggs, especially protein-wise and extra calcium for the egg shell.