Will My Hen Still Lay Eggs After She Has Already Had Fertilized Eggs?

No... If a chicken is brooding (sitting on a clutch of eggs)... She'll stop laying.  That's why eggs are collected regularly if you don't want chicks (some hens will brood a clutch of even if the eggs are not fertile.)   Hens will only begin brooding once they get clutch together (usually around 8-12).  When you remove the eggs as she's laying... She keeps laying thinking she's putting a clutch together... Once she feels she has enough eggs together at once, she'll stop laying and start to brood.

Hens can lay eggs without a rooster. Fertilized eggs do taste different to some people. When the weather gets cold egg production slows down and sometimes stops until it gets warmer. We have raised chickens for 25 years. One other piece of advice, if you move your chickens they will stop laying for a short time due to stress.