For instance, if your mom has passed away and is in Purgatory, can she see her children on Earth? Can she hear their prayers to her?
We don’t know exactly how this works. We only know that the saints (those in heaven and those being purified before they enter heaven) see and hear whatever God permits them to see and hear.
We just have to have faith and trust in the mercy of God, who surely will do whatever is best for us and for our departed loved ones. And of course we should pray for them.
I remember that some saint claimed that they can see us when we pray for them…but can’t remember who…but I guess what matters is that we do pray for them.
As for your Mom…how much we want to know we are still in contact with our dearest ones…
My Mum died in 1965, but still in some of my worst moments I find myself saying, “Mum, please pray for my boys. Please pray for me.” I think God ‘gets’ the sheer need and trust in those moments we call on those whose love as humans we most relied upon.