>As you said space expands f>I know as a fact that the expansion of space is faster than the speed of light. But how do we know that?

We know that space is expanding faster because of the dipper effect. You probably are most familiar with how a siren sounds differently to you if it's approaching or moving away from you. Well light has that effect too. So we see that the light is shifted to the moving away from us. The objects farther away from us has a greater shift in their light than closer objects. So that's how we know it's moving faster than

>How do we know that the observable universe is 90 billion light years across. Wouldn’t it take 45 billion light years for the light to reach us? (assuming we are at the center for argument sake) If the universe itself is 14 billion years old, wouldn’t we have to wait another 31 billion years to know the space expanded?

When the light left galaxies, they were 14 billion light years away but now they are 46 billion light years away.

Try to imagine you are standing on a road in front of you every meter there is a person standing, behind you there is also a person every meter. The road starts to expand so now there is an extra meter between every person. So the person 1 meter in front of you is now 2 meters in front of you. The person that was 10 meters from you is now 20 meters away.

Put another way the farther away someone is the faster they appeared to move despite no one moving at all

Now imagine there a car on the road as it sets out we know how far away the destination but as they arrive at their destination we see that it takes longer than it should have because the road expanded while they were moving. Some destinations are so far the car won't ever reach it no matter how fast they go.

If a similar car was coming towards us and we could observe (we couldnt) it would appear like the car was moving away from us even though it's clearly moving towards us.

So for your questions even though the light was emitted 13.8 billion years ago the space between where it was emitted and where we are has expanded since that time and they are 46 billion light years away.