Your team power is based on the champions in that specific team - their stats, level, ascension, booked skills, Masteries, artifacts (stars, level, glyphs), Great Hall and Arena Tier bonuses. Each team has its own power value, indepepndent on any other teams you may have put together. Your Arena team may have power of 120,000, while your Spider team may have powwer of, say, 150,000, because they contain different champions with different setups.
Unused Artifacts and glyphs do not count towards a specific team's power.
As for the skill books, join a clan and start hitting the Clan Boss every day. You can get 4 Clan Boss keys for free every 24 hours. They replenish 1 key every 6 hours, but only if you have 0 or 1. If you have 2 keys already (or even more from some rewards, etc.) you won't get any more, until you use enough keys to get below 2 keys. Clan Boss chests may contain skill books among the other loot.
Unless you have already maxed your Gem Mine, do so as soon as you can. Do NOT waste your Gems on Energy or anythign else until you have maxed out your Gem Mine and preferably also unlocked all Market slots. The sparring pit slots will also save you lots of energy.