Clues:
1) The trackpad seems raised above the level of the deck.
2) When you close the "lid," the gap between the display shell and the mail chassis is uneven.
3) The normally hairline gap between the chassis and its bottom plate is large and uneven.
4) One or more bottom plate retaining screws have gone missing or were found loose on the desk.
5) when you place the computer on a known flat surface (solid-surface or granite countertops work well for this), the computer rocks, with only three of the four rubber feet touching the surface at any time.
As WheelieNick wisely advises, if you suspect any issues with the battery, immediate service is needed. If the battery starts to swell, that progresses quickly with big, visible daily changes. Forces are strong enough to bend metal. Ignored, swelling can damage the computer beyond practical repair.