1. You shouldn't have a product in Line Item that isn't picked from the products table (layout). You can script if you what you type in a type-ahead situation yields no record, have you pop up the products table, create new record, commit, and drop it into line items
2. I don't think your method would be recommended. Best to control the price in Products, with a calculation or lookup to line items. Then you can change the price in line items manually and not have it effect any other invoices.
If you have to do it your way, a set variable (line items price), GTRR in Products, Set Field (the price field from the variable) may work. I would try it on a copy first
I agree with Steve. If you are going to change a price such that all new line items for that product should now have the new price, it should be done in products, not line items. The same for adding a new product. If necessary, you can set up a popover on your layout for creating a new products record where you can then enter data into the appropriate fields of the new record.
Thank you STEVE MARTINO and PhilModJunk for the advice!