Doughnutman,
If there's "pain", even for the first time, then there's something wrong and one should immediately stop. If the "pain" is recurring and/or isn't subsiding after a little rest, then it's time to see a specialist to determine what's going on and what can or should be done about it. If the pain or discomfort goes ignored, that's when the real problems set in. Unfortunately, pitchers in HS and even many in college will "suck it up", which is a good receipt for ongoing arm problems. And if you have an elite pitcher and ignore any pain or discomfort issues, then that's just stupid.
Yes, ALL pitcher push off the mound. But it's not a push like one might think of in terms of a sprinter pushing off starting blocks. But TPM is correct to point out that it's NOT a good idea to get the pitcher thinking of "pushing off". The actual amount of force on the push is actually very small and of itself doesn't do much of anything except to enable the pitcher to achieve his stride. IMHO, it's better to get the pitcher to a landing spot at the end of the stride than to think about "pushing off."
Whether pitching or hitting, the "lower half" is the foundation that the upper half sits on and follows. If the lower half doesn't work well, then . . . .??? Strength and conditioning (developing) of the lower half is key in controlling the upper half and maintaining control over time. So, as I mentioned about the amount of force involved, I'd say "developing" the lower have doesn't do much to increase "push", though it can help with lengthening the stride that is affected more by a different set of muscles than those used to "push."
The "slot" can be successfully changed without adverse results, such as developing injuries and pain. It's just that when a slot is changed, there's so many other things that need to be changed with it to accomodate the new arm position. This is why TPM's advice is GOOD when he said "stay away from anyone that wants to change your sons slot, unless he is experienced in doing so."