I would add depth to that bed across the front of the house. straighten the curves and only have them where needed to allow space for a wider plant such as the palm. As is it is adding to mowing difficulty, but not adding to the aesthetics. Set the edging bloom into the soil as a mowing strip and use a brief solid edging to keep grass from growing into the bed. The current arrangement will require a lot of trimming of grass and removal of grass that tries to creep into the bed.

I would move the palm further from the wall. It is already just about touching the wall which will shred the leaf when it happens during wind. I don't know anything about this particular plant, but plants do grow, so look up on a reliable source the 10 year size, add a couple of feet to allow you to do things like paint the building behind the plant, and then replant. This may require an outward curve of the bed edge, but there will be a logical reason for it. Long sweeping curves look better than wiggles.

For the bed next to the walk, if you will be replacing and widening it in the next five years or so, I wouldn't put a lot of money into it. 4' isn't widen enough for the vast majority of shrubs. They grow and then will start crowding the already narrow walk, not a welcoming look for visitors. Look for a billowy but not wide perennial. If it were mine, I would instead be more likely to leave most of the plants that are already there, just removing those at either end. Set down a concrete tile at ground level and add a tall pot at each end with some plants with bright flowers or leaves.