How to copy each result to other column when accepted?

I am looking for help from exports.
In attached sample sheet, F3 is the result cell. When "select" button next to the cell is activated I want this result value copied to selection list cell E7 (paste special).
Continuing with next result F3, and "selected" I need this new result copied to next column on selection list E8 and so on. How do I do this?

Next task is to remove any selected items (that were copied from various results) when "remove" button is activated and below items should move up to fill the blank cell.

F G
<1> choose--> Category A
<2> choose--> Size S
<3> result--> Model A-S select button


Selected Model (from f3 result. whenver G3 is selected new result copied to below list)
<7> Cell E7 (f3 copy here) remove button
<8> Cell E8 (f3 copy here) remove button
<9> Cell E9 (f3 copy here)
<10> Cell E10 (f3 copy here)

Looking forward to experts guide.

Thank you in advance.

Wow, so fast and nicely done. However, I need to make first selected result stays in the list. Then when new result is selected it should copied to next column upon selected. Currently, reult value copied to E7 does not stay and keeps changing with new result. Any other method?
You can disregard the QTY. It is for user to add when ordeirng selected items.

In general, here is my scnario.
E1:F3 is for selection of many products and the model number is the result at F3. If OK user can click "select" button and it should go to the cart (E7:E13). User needs to select more items and keep adding them to the cart.

Super!!!!
Thank you sooooo much!!

Simarui, I've been struggling for a week with this and you solved it just in a split seconds!!
Both work perfectly per my needs. I am so lucky to find you here today. Thank you again.