Backfiring (https://www.yourmechanic.com/article/what-causes-a-car-to-backfire) is often caused by a too lean or too rich air-to-fuel ratio although a few other causes are discussed below. A backfire in the intake manifold is caused by a ratio that is too lean (not enough fuel)....
The oil pump in your transmission is probably worn out. The oil pump produces the hydraulic pressure that the transmission uses to engage the forward clutch. As the transmission warms up and some of the clearances tighten up, there is...