1. I think your sentence is correct, using ～に います. For addition, you can put particle ~よ at the end of います、means you are telling person that doesn't know about that. But, we can use this to friends, i think in this case if we put ～よ when we talk to teacher it considered to be impolite. sounds like "hah you don't know that, sensei".
2. My grammar teacher told me ～て is used as a connector between one verb and another verb, or one adj to another adj. And ～てから is used for the order of two activities. After~ , you do other thing. e.g 朝ごはん食べてから、新宿へ行きました。 After I had breakfast I went to Shinjuku.
hope these help