"Tip-in" means a slow, small movement of the gas pedal off of idle. The typical story would be, "it has a slight tip-in hesitation or sputter, but it runs fine under harder (normal), acceleration, like when leaving a stop sign. That happened more commonly years ago with carburetors.
"Bump kick" sounds similar to the more familiar "bump shift". That occurs on computer-controlled transmissions when it waits too long to downshift to first gear when you come to a stop. If you accelerate again just as that downshift occurs, you feel a bump or jerk as it grabs first gear as the engine speeds up. It's more irritating when you do a rolling stop through a stop sign without coming to a complete stop. That can be a little stressful on rubber engine mounts, but it's mainly just irritating.
"Torque shaping" sounds like an advertising term for how some Engine Computers modify ignition timing and / or fuel metering to reduce engine power at specific times. I drove a Ford Taurus rental car that did that every time the transmission up-shifted. It was extremely irritating to drive a car like that as it always felt like the engine was cutting out. One Ford mechanic said they had to do that because the transmissions were so poorly built that they couldn't hold up to the stress of shifting while under hard acceleration. Stop and go traffic is hardly the place for hard acceleration, but that's where we felt it all day long.