Sometimes the AI (artificial insemination) gun passes freely through a heifer’s cervix; in other cases, it just meets a dead end. So, in this case, should I deposit semen just inside the cervix when the gun cannot pass through freely?

More than likely you are either hitting the blind pouch, which is formed where the front end of the vagina joins the back end of the cervix, or you are getting stuck in one of the circular rings of the cervix. These are the two biggest obstacles. Trying to manipulate or stretch the cervix with your palpation hand will help. Make sure that you are also keeping your gun at an upward angle when inserting it into the vagina so that you are not entering the bladder. To achieve the highest possible fertility rate, the semen needs to be placed at the very front (internal) end of the cervix.