In most cases, yes - just make sure that the phone you order/buy is unlocked for your particular network (they should confirm this when you order/buy it - although most 'SIM free phones tend to be fully unlocked).
Yes as Cupra says you can but be aware that this is buy far the dearest way of buying a mobile esp. if buying new from a high st. retailer.....try a shop likes of cash converters or similar first who tend to get quite up to date phones and sell them a fair bit cheaper.