Can I set shipping by the number of items, like one price for 1 to 3 items and another for more?

Yes. Use a Quantity-based (brackets) method in the Shipping Zone plugin:

1. Go to Plugins → Shipping Zone and click Edit on the zone.
2. Click + Add method and set Type to Quantity-based (brackets).
3. Click + Add bracket for each range and fill in Min qty, Max qty and Cost. Leave Max empty on the last bracket to cover everything above it.
4. Add a Label and click Save zone.

For example: 1 to 3 items costs 50, and 4 or more costs 90. Make sure your brackets have no gaps, because a quantity that fits no bracket is charged nothing.