When do you omit the い? Is it ungrammatical to use してる?
It is technically ungrammatical in written texts (my Japanese teacher back then used to remind us often about that). Technically, it's part of the so-called "casual" style in the Japanese language. That is, い is often (almost always) omitted in casual conversations among friends or same-level people.
However, it is quite commonly accepted now in (some) texts as well as it reflects as I said the casual conversational style.
Maybe the fact that is so often found in written texts nowadays is a legacy of the IT-revolution (let's call it this way) of the past decades. With the advent of modern technologies and the exponential increase of instant messaging, people just started naturally to "write the way the speak" more and more often.
I would say that, in a way, it could be compared to how some kids write texts using abbreviations such as "idk", "ttl" or.. "wtf". :D