Every time my friend's neice sends me a mesaj, she writes ' seni seviyom ' instead of ' seni seviyorum '. Is this like saying 'Love ya!' instead of the formal 'I love you'?

Could you apply it to other words like istiyom,etc..

Just wondered,thanks xx

While there is nothing wrong to pronounce them as your friend did this shouldnt change the writing. But you understood the issue very well as your both examples show.
So, yes it is like the English phrase, and yes we can apply it to other words exactly as you did.

To be honest it sounds funny, very young and natural but for us teachers its like something that makes the alarm bells ring when seen as a written text.