Re: installing apps.
By default Android installs apps in the internal storage area not the SD card.
To create space in the internal storage area, move all 'your' data e.g. music, pictures, videos etc to the SD card.
Once the app has been installed you can check if it can be moved to the SD Card (Settings > Apps > Downloaded Apps > scroll to find app, tap to enter app > check if Move to SD Card is an option). Sometimes apps cannot be moved as the app developer may not have given permission when the app was created.
If SMS have you checked if they have been sent, are they the same text repeated, are they to the same contact, can you delete them?
If MMS (text with pictures, videos etc) do you have 'data connection" enabled (usually Settings > Wireless and Networks > more > data connection)? If not you are 'offline' and MMS won't be sent, (i.e. this is for internet and MMS, NOT for phone and SMS)