I am using an Arduino Uno R3.
It is not clear on the schematic whether there are pullups on the A4 and A5 I2C pins.
Are there hardwired pullups or do I have to add them myself?
There are very weak internal pullups, but they are not strong enough to be considered compliant with I2C specs. Supply your own external 2.2k-10kohm pullup resistors.
No. There are potential internal pullups, but not AFIK activated.
You can quite safely connect I²C to Raspberry P1 (3.3V).