FrogReaver
The most respectful and polite poster ever
1. Well, you cant use it that much as you cant use it on huge or larger creatures. It does compete with your bonus action usage, on my current Paladin its about %75 of the time as a guesstimate.
2. I would say that's about right. With the feat you will max your STR score sooner rather than earlier and it is an opposed check.
3. Correct, you and your rogue or monk or paladin or barbarian.
Of course this would take a little work, and would not include staying power of +2 to AC and the rest of the shield master benefits to saving throws. A lot of the work has been done here already. https://1drv.ms/b/s!AtVzM7E-c0rph61NMMkxGZD9ojIyTw
BTW, the ability to prone or push ANY size is what makes open hand monks by far the best IMO. Its not as flashy but proning to set up the team or at least halving their movement is useful. There are a bunch of huge and tough creatures in the game with poor DEX saves.
So I used the assumptions listed and looked at 2 level 10 characters since that's all our assumptions required. The first a basic sword and shield fighter with shield master and duelist style. The 2nd was a level 10 barbarian with GWM that didn't use reckless attack. I didn't calculate anything related to crits but the impact should be fairly minimal.
What I found:
Shield Master Increased party DPR by a minimum of +5 and a maximum of +7.5 (depends on AC and skews closer to +7 overall if I had to nail down a single value).
Again this was following our assumptions outlined above.
It's a nice bit of DPR. No where near the SS + CE combo but for a single feat vs 2 feats its not bad. Of course it's a little more finicky as their are a lot more variables that impact it's usefulness over the CE SS Battlemaster Fighter.