Can facebook show that someone is online when they are not and visa versa?

[mariana]

Whenever I am on Facebook, it shows that my friend gets on and after 5 minutes gets off and then 5 minutes later gets on again until finally after 30 minutes he/she is off. Are these guys ignoring me or is this a common thing in fb?
Then whenever i chat with my friends, it says the person is typing, and when the person "finishes" I never receive a message. It says that it has been seen. R these friends of mine ignoring me? Are they sending a message that I am not receiving? Idk wats happening.
Please help I'm new to facebook

[Andy Huynh]

Well they could be using the facebook mobile app.

[Emma]

it depends if they logged out or not