Yes and yes.
All of Christianity hinges on the answer to this question. If there was no resurrection, there would be no Christianity. Consider this: there were over 500 witnesses to Jesus’ return to life after being crucified dead and buried. The Romans made no mistakes when they killed someone. They were expert at the art of death. Yet, three days later, Jesus appeared to his disciples, to several women, to two men walking on the road to Emmaus, to a doubting Thomas and two others. Jesus was definitely dead and he was definitely resurrected.
His disciples witnessed his ascension into heaven. So yes, Jesus is definitely alive. It is his power and authority that holds every atom in the universe together. One day Jesus will return to earth just like he left it to rule and reign as King of kings. Given the events of these times it could even be soon. Are you ready? (see Matthew 25: 30-35)