Well, to summarize your concern
Yes, original ang parts ng mga ganyan, pero sometimes meron dn refurbished, nalaman ko ito sa kakilala ko na nagbebenta ng secondhand phones, refurbished means although original ang parts pero hnd ito ung stock parts nya.. its some what assembled cya sa mga original parts, pero the thing is not all naman daw.. hindi mo ito malalaman thru physical insepction by looking sa device, kailangan mong buksan.
Sa battery no issue naman doon. Kasi orginal na iphone dn yan.
With regards sa gpp lte, double check mo cya tlga ha.. make sure na lte tlga, kasi roughly and commom to gpp phones hnd lte thru certain carriers