This one sentence has been leaving me stumped as of late.
For context, it refers to a soccer player who went around injuring his rivals. I think it's the 年齢的に and 選抜に残る that are really throwing me off. Anyway, the best I can come up with is: "He was driven by a sense of urgency, as his age made this the final year he could be drafted for the national team."
I think your translation is correct.
的 can be added to a word same as the suffix -wise is added in English. So 年齢的に = age-wise, in terms of age, speaking of age, etc.
全日本選抜 depends on the context. I've seen various invitation tournaments referred to as 選抜, so this could also mean "national invitational championship". But then again, it could be what you translated it as.