Can teachers tell when a student likes another student?

Oh, yes. Looks, smiles, sideways glances, scribblings on the notebooks, rapt attention when the other person is speaking- there are many ways to tell. 

There are always exceptions but teachers tend to be more aware of things than snotty nosed kids could ever imagine.  How?  Experience, education, and paying attention to what goes on in their classroom is what they get paid to do.