That poor guy has really gone through the ringer. The injuries don't look recent and seem to have healed up nicely. Whether he is a male or not, it is likely his hemipenes have been amputated along with the tail (though it doesn't look like that tail was removed by a Vet, but due to injury...either fight with another bearded dragon or another animal).
Other than the old injuries, he seems to be healthy. Getting him to a vet to make sure there are no underlying problems, wouldn't hurt. My biggest concern will be the vent area, but if he is pooping fine without straining he should be fine. Making sure he is getting enough food will be important though as one of the primary fat storage areas is gone (ie tail) so prolonged periods of no food or insufficient food, can be very dangerous for him.
I also suggest to keep him off any abrasive substrates (ie sand) and use low wide basking spot, so he can climb them easily. With three good limbs though, shouldn't be much of a problem climbing and moving about.However with no tail, which does play some part in balance, he may not like narrow basking areas.
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PHLdyPayne