Look at multi-flow drainage systems on google. You need drainage. It probably should have had a wider footing going back toward the slope (called a cantilever wall - the backfill sits on the footing like a fat guy on a chair so that the back of the char can't tip over). He built what is called a "gravity wall" which relies on the mass of the wall being greater than the force of what is being retained so that it won't move. Any water build up behind that wall causes what is known as hydrostatic pressure which adds to the force being applied to that wall. Weep holes would have been a good idea during construction. Now it is a bit more difficult to make the weep holes. At minimum, put in drain pipe and clear drainage stone behind the wall so that the water can get out. What was built is a typical basement wall built to support something on top of it and with a structure holding the top of the walls apart and a concrete slab holding the bottom of the walls apart. He is essentially asking a vertical slab to hold back 40" of fill without pushing out or toppling over.

Because dry-stack blocks aren't a precision building material in terms of tightness of fit, particularly going around curves. If you don't believe me about how these blocks are put together, just lift several of them off: I bet you don't see any residue of mortar or glue, which is normal. You could have loose blocks for any number of reasons, including soil settling, animals, kids running around, frost heaving, or an incompetent wall builder. I'm not saying you can't mortar or glue a loose block, but, if you ever need to rebuild or modify the retaining wall, it will just make the job harder. I have a wall similar to yours and had to take it apart in one place to combat soil settling. I unstacked some blocks, added gravel to the base, and reset the blocks. Years later, it's still fine.

to expand on what I said - there's no fixing this. This is built by someone lacking a fundamental understanding of how to build a cmu retaining wall. It WILL fail. Here's a detail drawing of how it should've been built, per a local county's typical wall guidelines. Whoever you hired is incapable of the work.

Remove the damaged blocks and clean out the entire cavity completely before trying to insert the new block. If there very tiny encroachments keeping the new block from seating properly, try soft taps with big hammer (which might be a block of wood or similar.) A hard hit with a steel hammer might chip or crack the block.