Liberal communities are always delighted to welcome a new baby.

As well as lots of kvelling, there will be thanksgiving prayers and the baby will be given a Hebrew name.

Yes. Liberal Judaism affirms the equal status of boys and girls.
They certainly can.

Although, please speak to your congregation’s rabbi as to how your partner’s commitment is expressed.

It may well still be possible to have a thanksgiving service for the life of a new child. You will need to discuss this with your local rabbi.
If the adopted child is a baby, then a baby blessing would be appropriate.

If the child is of an age where this is not considered appropriate, there will certainly still be a way to welcome the child into the community. Please discuss further with your local rabbi.