I am not mocking acts of God because I do not believe they are acts of God. Even though God can heal today I would say that 90% of healings today are bogus. They are either fakes, such as the common leg-lengthening trick, or not miracles at all. Supposed healings that take days or months to occur are not a miracles. Nor are slight improvements in a persons condition that can be accounted for by the natural healing process. The 'healings' that today's faith healers claim to perform are usually unverifiable illnesses such as back pain which are known to be improved by psychosomatic techniques and the power of suggestion. Others are outright frauds such as the leg lengthening parlor trick popular among the charismatic charlatans of today. It is purely an act. There are several Youtube videos that explain how it is performed. If they can supposedly grow limbs on demand then why are they not restoring the limbs of amputees?
I only have your word about you and your daughters healing and don't know enough details to determine whether was a genuine miracle ie. something that defied the laws of nature (eg an amputated hand being restored, or a visible tumor suddenly disappearing) - but I will presume it was. You said it involved prayer. Wonderful, your prayers were answered. I believe in those kinds of healings. But praying for healing is not the gift of healing. If people have to pray for healing it proves they do not have the gift of healing. If they had the gift of healing they would be able to instantly and completely heal people of serious disabilities simply by a command or a touch as the disciples did in the New Testament. They didn't have to pray for healing. They could heal people instantly because they had been given that supernatural ability.
But certainly God can and does perform miracles today in response to prayer. Would I pray for a friend with cancer to be miraculously healed? Sure I would. Would I expect the tumor to instantly disappear without trace? It has happened before so I would be hopeful, but as the millions of Christians with cancer would testify, God does not normally operate that way. Despite intense prayer, many of them are not healed and will often go on to die from their illness. Thousands of charismatics prayed for John Wimber, the founder of the Vineyard church, but he was not miraculously healed from his cancer. He had to have radiotherapy. Nor was he healed from his heart disease, and had to have open heart surgery. Shortly after which he died at the premature age of 63. So much for faith healing in the charismatic church.
You are absolutely right. Jesus did perform miracles so that we can believe he is the son of God. As your quote from John 20 says, they are recorded in scripture for everyone to hear and be convinced. Therefore we don't need any more supposed miracles today in order to believe in Christ, especially dubious ones that don't even come close to matching Jesus's miracles. We just need to hear the scriptures. As it says, faith comes by hearing the Word of God. The gospel has been effectively preached in this way for the last 2000 years without 'signs & wonders'.
I can't say I've heard of Angus Buchan before. But I googled his name and
his Wikipedia page says he preaches the prosperity gospel, makes claims of healing that are unsubstantiated, and has allegations of financial impropriety. So much like Benny Hinn, Kenneth Copeland, and the other charismatic charlatans of today it seems.