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