Eggs – Do you add extra oil when replacing eggs in baked goods

Butter is at most 82% oil and the rest is water. So, you're going to need to add more butter for the same amount of oil. Besides, you need to adjust the liquid content accordingly since you are going to have more water than you planned.

If you are going to use the same amount of oil, then it will not make any difference other than the taste. Just make sure they are of same state (i.e. melted butter instead of vegetable oil or vice versa)

It's certainly safe. Butter, Oil, whatever, it's more about taste than anything else. Some people even push lard and butter as the "safe" options, because they require less processing than oil, and much less than margarine.

One thing which you should be aware of in regards to butter vs oil: butter has a significant amount of water in it, so you shouldn't substitute 1-to-1, or you will have a stronger flavour (and more fat) than perhaps you want.

If you're accustomed to salted butter, adding some salt will help ease the transition. If the flavour of olive oil is off-putting, there are plenty of more neutral flavoured oils that have a similar fat composition, or you can simply avoid extra virgin olive oil*.

*extra virgin olive oil in the U.S is largely a scam. In most of the world (countries that adhere to the IOC standard) this signifies "First Cold Press" olive oil. In the US it signifies "lamp grade olive oil with green food coloring". There are no restrictions on the use of terms like "extra virgin" in the US, so you can't guarantee that's what you're really getting just because it's on the label.