It's not a baby, as it has the yellow Iris around it's pupils, and that doesn't happen until a Senegal is at least a year old, if not older. Prior to a year old their eyes are completely black. So this bird is at least a year old, probably older. There's no way to know how old they are once their eyes change to having the yellow Iris, other than they are at least a year old. It would be on the word of the current owner as to the age and gender, as you can't tell a Senegal's gender without a DNA test by blood or feathers...
There is something going on with it's feathers, and it appears to be over-preening or plucking by the bird. My Senegal just went through his yearly molt that he has every spring (he's 3 years old now and I brought him home from his breeder at 10 weeks old and just barely weaned), but that is not just regular, normal molting that this bird in the photo is going through. He/she is obviously plucking, or at least over-preening...Usually this is due to a number of issues combined, anything from a poor daily diet to not getting enough attention and just plain boredom, to possible illnesses and diseases.
***The bottom-line to ANY parrot you adopt from their former owners like this is that there is absolutely no way to know whether or not the bird is sick with anything from a simple bacterial or fungal infection to something potentially lethal like an Avian Viral Disease...You just don't know. You never know, that's one of the risks that you take whenever you adopt ANY parrot from their former owner...You have to believe what the owner is telling you about the bird's history, such as how many owners it has had, where it came from originally, it's medical history, it's behavioral history and any behavioral issues or medical issues it has had in the past or currently has, what it's diet consists of, what it's personality is like, what it's level of tameness is like, etc. Sometimes people tell the 100% truth, sometimes they lie through their teeth about every little detail because they just want the bird gone or because they need the cash quickly. You just never know.
As such, all you can do is look at the bird and take note of visual signs of issues, and then go and actually meet the bird and interact with the bird one-on-one, and I'm talking spending a good few hours with the bird, not just 10 minutes before you hand them the money and load-up the cage into your vehicle...Also, you should be allowed to pay to have them take the bird to the Certified Avian Vet or Avian Specialist Vet (no Exotics Vets for this) of YOUR CHOICE, never of their choice or to their current Avian Vet if they have one, in fact don't take him/her to their Vet purposely because you want a 100% objective opinion, and then have a full Wellness-Exam done by the Avian Vet that includes a full physical and visual exam, a full Fecal Smear that includes Microscopy in the office on the spot and also then sending a culture out to a lab, and then routine Blood-Work that will show you if the bird currently has ANY infections, is Anemic (indicates a bad diet and possibly Metabolic Diseases), and most importantly a Liver and Kidney Panel done to test both of their functions...And in this case I would also add an external culture/swab of the bird's skin to be looked at under the microscope right there in the office, because often a very common cause of either over-preening or the start of plucking is actually a topical skin infection, etiher by a bacterium, or more-likely a huge topical Yeast infection. And if the current owners won't allow you to pay for a full Wellness-Exam with testing done, then you'll know there is a medical reason they don't want you to have it done...
***There's no way to know whether a bird is fully healthy or if it has any behavioral issues, you just have to go with what you can tell by both looking at them visually and then what they are like when you spend a good couple of hours with him BEFORE adopting him...All we can tell you for certain about this Senegal is that he/she is definitely over a year old due to his yellow Irises, and that he is at the very least over-preening or at the start of plucking himself due to some reason unknown.