割引 and 無料: discounts and no charge
Read the difference between a reduced price and no charge.
Reducing a price
割引 (わりびき) is a reduction from the original price. 「一割引です」 means 10% off, so an original price of 1,000 yen becomes 900 yen. Do not confuse the discount rate with the percentage still payable.
「割引前の値段」 is the price before a discount, and 「割引後の値段」 the price after it. Missing 前 or 後 changes the amount used as the reference.
An item with no charge
無料 (むりょう) means no charge for the specified item. 「見学は無料です」 says that the tour itself is free. Unlike an ordinary discount, it sets that item's charge at zero.
「無料で配ります」 means distributing something free of charge. 無料で indicates the absence of a charge, not the quantity each person may receive.
Reading the applicable conditions
「会員は二割引です」 says that members receive a 20% discount. It is not a free event for all visitors. For either discounts or free offers, read any separately stated eligibility and period.
「割引は今日までです」 says that the discount lasts through today. It ends the discount period, not the shop's operation.
Does 「半額」 mean free?
Show the answer and why
No. It means half price. An original price of 2,000 yen becomes 1,000 yen, not zero.