Does the wolf lose its trip?
According to the SRD the stats of animal companions may change when they advance. For example a wolf on level 1 has Attack bite (1d6 plus trip) on level 1 and Attack bite (1d8) on level 7.
Does it lose the trip ability after leveling up?
No, this is an erroneous omission on the part of the d20pfsrd.org editors. To quote the Core Rulebook on the Wolf, from page 54, the Wolf explicitly keeps its trip at level 7:
Starting Statistics: Size Medium; Speed 50 ft; AC +2 natural armor; Attack bite (1d6 plus trip); Ability Scores Str 13, Dex 15, Con 15, Int 2, Wis 12, Cha 6; Special Qualities scent.
7th-Level Advancement: Size Large; AC +2 natural armor; Attack bite (1d8 plus trip); Ability Scores Str +8, Dex -2, Con +4.
How's that Natural Armor Bonus work?
Also what does AC +2 natural armor mean in the advanced version? Is the natural AC still +2 or incremented by another +2?
It's incremented by another +2 at 7th level. To quote part of the explanation of how Animal Companions work on p52, within the Druid class's pages:
Natural Armor Bonus: The number noted here is an improvement to the animal companion’s existing natural armor bonus.
It's worth noting that the wolf's initial natural armor bonus is a +2 on top of the natural armor bonus already granted by Table 3-8: Animal Companion Base Statistics on p52. A 3rd level animal companion already has a base natural armor bonus of +2, so if that animal companion is a wolf, it gets a further +2 to its natural armor bonus for a total natural armor bonus of +4.
At 7th level, a wolf's natural armor bonus is +8: +4 from its animal companion base statistics, +2 from wolf level 1, and a further +2 from wolf level 7.