The male's beak looks to be a bit long and could use at least a filing by a Certified Avian Vet, but in-general their beaks look fine. Their beaks appear to be healthy, no mites or anything like that, just a bit long.
If your birds are acting lethargic, meaning they just sit around all day long, or they are sleeping more than usual, that is an indication that they may have some type of illness. If they are eating less than they normally do or not eating or drinking at all, if they are sneezing/coughing or have any liquid coming from their nostrils, if they are sitting on the bottom of their cage, or if they are "fluffed-up" all the time, then these are also general signs/symptoms of illness...As far as their droppings go, if they are at all runny/watery and it can't be attributed to them just prior eating fresh veggies or fruit, or their droppings are "black", this can also be a sign that they have some type of illness, such as a bacterial and/or fungal infection.
The only way to know if your birds have an illness is to find an Avian Veterinarian and take them in, and have them check their droppings from bacteria or fungi/yeast. Don't attempt to give them any medications yourself until you know if anything is actually wrong with them and what is actually wrong with them, because you can make them much worse if you give them the wrong medication.
If their only symptom of illness is that they aren't being very "active", it may be because they are just simply bored...Do they get much time out of their cage every day? And do they have lots of different toys inside of their cage to play with and to keep them busy? If not, then most likely they are just very bored and need to have lots of different types of toys and foraging activities to do inside of their cages, and they also need to get as much out-of-cage-time as you can give them every day to keep them from becoming extremely bored. Budgies are extremely intelligent, they have the intelligence of a 3 year-old human child, so they need lots of things to do and play with to keep them busy. They are also very social parrots and they love to get out and about, so letting them out of their cage together every day so they can get some exercise is also very important.