did our early church Leaders believe healing or the "gifts of the Holy Spirit" stopped with the apostles?
no they did not, why should we? Let us take a look at some of their writtings
Daily some are becoming disciples in the name of Christ.....who are also receiving gifts, each as he is worth. These are illuminated through the name of this Christ. For one receives the Spirit of understanding, another of counsel, another of strength, another of healing.
justin martyr (c160, e)1.214
For numberless demoniacs throughout the whole world, and in your city, many of our Christian men. exorcising them in the name of Jesus Christ, who was crucified under Pontius Pilot, have healed and do heal, rendering helpless and driving the possessing devils out of the men, though they could not be cured by all the other exorcists, and those who used incantations and drugs.
Justin Martyr 2nd apology, chapter 6, addressed to the Roman senate, Ad 165
Those who are truly his disciples, receive grace from him,....perform works in his name, in order to promote the welfare of others, according to the gift that each one has received from Him. Some truly and certinally cast out devils. The result is that those who have been cleansed from evil spirits frequently both believe and join themselves to the church.Others have foreknowledge of things to come: they see visions, and utter prophetic expressions. still others heal the sick by laying their hands upon them, and the sick are made whole. What is more, as I have said, even the dead have been raised up and remained among us for years. What more can I say? it is not possible to name the number of gifts which the church throughout the whole world has received from God, in the name of Jesus Christ,
who was crucified under Pontius Pilate, and which she exerts day by day for the benefit of the Gentiles, neither practising deception upon any, nor taking any reward from them [on account of such miraculous interpositions]. For as she has received freely from God, freely also does she minister [to others].
irenaeus (c180, e/w) 1.409, Irenaues against heresies, book 2, chapter 32, section 4, Ad 200
Irenaues against heresies, book 2, chapter 32
And some give evidence of their having received through this faith a marvellous power by the cures which they perform, revoking no other name over those who need their help than that of the God of all things, and of Jesus, along with a mention of His history. For by these means we too have seen many persons freed from grievous calamities, and from distractions of mind,and madness, and countless other ills, which could be cured neither by men nor devils.
Origen against Celsus, book 3, chapter 24, Ad 250
Clement ordored those to approach who were distressed with disease, and thus many approached having come together through the experiences of those having been healed yesterday, and he having laid hands upon them and prayed and immediatly healed them
Clement, homily 9, chapter 23, 3rd century
this list could go on and on, not only was healing a part of ministry work in the new testament, but it was also within the church after the new testament, and within the church today.