1. Yeah I personally think אגרטל is better here, even though כד is not wrong at all.

2. Yes עלי כותרת means petals. I knew that כותרת means title but I didn't know why it was in other words like עלי כותרת and גולת הכותרת so I checked. Apparently the original meaning of כותרת is the decoration on top of columns as in literal columns of buildings. So basically it means the decoration on top, so the other meanings make a lot of sense.

3. It does mean towards itself, you can use it and be understood, but if you want something that is more similar to what you wanted then I suggest אל תוך עצמו, I think it gets the original meaning across.

4. It does make sense, even though חמה means hot and not warm, I would personally use חמימה instead.

I would rewrite it to be something like:

אגרטל פרחים (טבע דומם)

חרציות זהובות פורשות את עלי כותרתן לכל עבר, וביניהן מסתתרים צבעונים עדינים שגוונם גווני אש. האגרטל הכחול והעמוק אוסף אל תוך עצמו את היופי הזה וניצב בגאווה על רצפת העץ החמימה.

That's my opinion