It is possible but in most cases silly and in more cases DANGEROUS. Just be careful!
You can form emotional attachments, of course, and even deep friendships. Just remember that people on the Internet can present themselves in any way they choose and you may be falling in love with a phantom. (Paedophiles are particularly clever at assuming a different identity.)
Here's a rule of thumb: "a man with moonlight in his hands has nothing there at all."
It's entirely possible. The person is assumably posting the pictures they look best in so your perception of his visual image is the best possible. Then again in texting, people have time to think and analyse their answers, enabling them to appear wittier, smarter, funnier. The only thing that's missing is body language, which may or may not have an impact towards your feelings for them.
Conclusion - Yes, it's possible, but you need to take under consideration the difference between the person's image in your head the the real them.
Bonus conclusion - women are more likely to fall in love over the internet, because our way of perception is different and we tend to give more weight to words than visual stimulation.
ONLY knowing the person on the internet?
1 - All you "know" about them, is what they choose to tell you. You have no way of knowing if they are telling the truth or not.
2 - Love is about actions, not feelings. It takes knowing the person and interacting with them in person.
It's possible - I met my current wife online - not on a dating site though, on a blogging site.