The raw transaction will take up more than the 160 characters a single SMS will allow, so you'll have to send a multi-part SMS or MMS.
In that case, just use a network connected phone to send your transaction using either Bitcon for Android or Electrum for Android. They both work fine for this purpose.
If that phone has been factory reset and has no other apps, it's decently safe. However, as others have said, the moment you intend to store thousands of dollars worth on such devices, a hardware wallet may make more sense.
A few people I know store up to 50 BTC on their mobile phone wallets. Depends on your risk tolerance, can you afford to lose your phone or have no backup or it gets stolen, or someone with a hacked wifi access point listens to everything .... public open wifi is not safe. Your own personal mobile data maybe safer, at least you're paying for it.
Yes but many people can't use their "data connection" on their phone when they are abroad and in many places there isn't 3G or 4G network, so sending your signed raw transaction on the GSM network by SMS can be a helpful solution.
