Effects that place a counter on a permanent include that permanent entering. For example, a creature that normally enters with one or more +1/+1 counters will enter that many +1/+1 counters on it. A planeswalker will enter with twice its starting loyalty counters.

Adding loyalty counters to a planeswalker in order to activate a loyalty ability isn't an effect, so those counters are not doubled.

Any -1/-1 counters that are placed on a creature because of wither or infect are also not doubled.

The chaos ability is cumulative. For example, if you roll twice in a turn, tapping a land for mana will cause two mana abilities to trigger.