Fellows here are right on spot! First the turquoise needs an urgent beak trim that must be done by a veterinary. Look, sometimes beaks overgrown due to poor diet that might affect the liver functioning. Of course changing the diet will help your bird to renew the beak to a more healthy status. Beaks as our finger nails grow all the time and after the health of your bird is reestablished the beak will grow a nice new layer from the nostrils toward the tip.
Please check with a vet for advice regarding the beak issues.
Regarding the ages, I would say both have less than one year. Older budgies will have lost their forehead stripes (like in the picture) as mentioned by Stormypica, still they are not that old as mature budgies? eyes tend to have a white ring around the pupill.
Considering they are both less than one year old, I would say they are not sexually mature yet. For that reason, the cere colour of their noses is pinkish. It is common for young males to have it pinkish before it turns blue, I think the turquoise is a male. However it is not that easy for lutino, albino or pied mutations. The yellow one is a pied mutation, which means the bird has only partially the expected markings. In such mutations, both male and female can keep a pinkish cere their whole life, however if you observe the nostril region of the yellow bird you can notice it is a bit paler than the turquoise. In that case, I would say it is a hen as the fellows here pointed out.
I'm new, so I'm not sure if I'm doing this reply correctly. I don't have my budgie yet, but I will within a few weeks. I really want to get a boy budgie. I'm a little nervous after hearing a few times that you may not know for sure the sex of a bird until it's about a year old. I've been looking around for a decent store to get a budgie from and I'm paying attention to the ceres of the birds I see. Some look clearly blue to me. I guess there's no way to know for sure? Am I right about that? Sigh... :20: