This is quite charming - I really like the pixel art in the game, and the flavour text made me smile
It feels quite different to Gussun Oyoyo (I played the Saturn version years ago) so don't worry about that too much!
I'd suggest changing the early levels to not restrict the mechanics available, since that makes them feel very hand-holding to me. (And starting with the light beam is nicer for placing things)
Also, it's confusing that on some puzzle-style levels (fixed set of blocks visible at the top) the Bot moves whilst you place the blocks (e.g. Day 4, Day 7), and on others he doesn't (Day 5, levels with the puzzle icon).
I felt like it would be better to have each level either being explicitly a puzzle-style (fixed blocks, Bot waits) or an arcade-style (unlimited blocks, Bot always moves) level. And use a different icon for the two types.
With that in mind, here's how I'd present the introductory levels:
Level 1. puzzle-style, 1 square piece to place to enable bot to get to the star.
Starting with a puzzle style level makes it easier to see that you don't control Bot (and also puzzle levels have fewer mechanics, since the light beam doesn't do anything; with a square block you don't have to know about rotation either), and I'm also not a fan of the first level having no interaction.
Level 2. like the current level 2, maybe with 1 more block to place to up the ante.
Level 3. First arcade-style level. Could be made easier than the current level 3.
As I mentioned above, I think you wouldn't lose anything by letting the player have the light beam and the ability to explode boxes here (with no crate boxes and plenty of space, explode doesn't change that much)
Level 4. Change to puzzle-type. (Minor detail: you can currently complete this level without blowing up the box if you hold left as you start, or if you use the "sky boxen" technique)
Level 5. Fine. Maybe make it a touch more complex (give the player two boxes with crates to be used) so it feels more like a puzzle.
Level 6. This one's good too.
Level 7. Making this into an arcade level might be a bit fiddly.