This is great to hear^^^ about to update my new summer grades next week and now I'm very excited toYes. When I applied way back when, I received a bunch of interviews almost immediately (like 1-2 weeks) after I updated my app with new semester scores.
And yes, an upward trend will matter, especially if you don't get in this cycle. Obviously if you do get in, they generally don't matter, provided you pass obviously.
I emailed a few schools based on what I had seen with other people's experience on the school specific threads, and ones I was really interested in, but many schools contacted me before I contacted them.