Translation:I like to lie on my stomach and watch TV.
«Люблю» is translated 'to love' only when it refers to people. When it refers to thing, we usually translate «люблю» with 'to like' (and for the English 'to love' about things, we use the Russian «обожаю»). At least that's how it is taught at school. :)
I have reported it anyway, as I think we use "love" about activities or objects rather more freely in English, so it doesn't seem an excessively gushy translation of "люблю". You can "love" anything - yes, even lying on your stomach, watching TV. It doesn't necessarily mean you are passionate about it. In some cases, it's barely any stronger than saying: "I enjoy".
Are you certain, or are they just commonly confused? In the UK, quite a few people say: "laying", when they actually mean: "lying". I think the confusion arises in part because the past tense of "lie" (in the sense of lying down) is: "lay". So it is correct to say: "I lay on the bed", if it's in the past, but never in the present. If you wanted continuous past, it would be: "was lying", not: "was laying".
"On the stomach" (or rather "on his/her stomach") sounds more natural to me. I don't really like "belly". Not quite slang, but rather informal. Of course, there may be times you want to create a more informal tone in your writing, but I wouldn't say it's the preferred form.
TVs used to be furniture items on their own that would sit on the floor, and yea you could lie on your belly on the floor and watch. To get an idea of what it looks like, you could watch the simpsons