1. Do you like shopping online?
你喜欢网上购物吗?
还能这样说：
Do you prefer shopping online?
Are you interested in shopping online?
2. Have you bought anything mail-order?
你在网上买过东西吗?
还能这样说：
Have you bought something online?
Have you ever done shopping online?
3. I purchase products or serives online at least once a week.
我每周至少有一次在网上购买产品或服务。
还能这样说：
I buy things through the internet at least once a week.
I buy products online at least once a week.
应用解析：
purchase and sale 买卖;
make a purchase 买件东西;
leave sb. to his purchase 让某人自谋生路;
not worth an hour's purchase 生命危在旦夕
4. Let's search online to find an appropriate cell phone.
我们上网找一款合适的手机吧。
还能这样说：
Let's buy an appropriate cell phone online.
Let's buy a cell phone through the internet.
应用解析：
appropriate to/for 适合，适用;
appropriate for 拨出(款项等)供……之用