Beneficial bacteria are not formed in your tap water or in the air. Cycling a tank can take weeks as the bacteria grow in your filter media. As long as your tank is heated, cold will not slow down BB growth.
You wil know when your tank has cycled when your readings are
When you had an ammonia reading without nitrate reading - your tank wasn't cycled. This is why your levels spiked.
If you decide to cycle your tank with fish- keep ammonia around .25 and nitrites around .25 until the tank has cycled.
It took me 6 weeks to cycle my tank with goldfish. I ended up doing daily 50% WC to keep ammonia and nitrites under control.
You might want to re read cycling information so you can successful cycle your tank.
As far as ph. Test the water out of the tap, let a glass of water sit for 24 hours and retest. You might find that ph is changing from this. Remember you can kill fish with a severe ph shift.