Answer to Q1:
I find number of times you practice can be more important than how long you practice. To improve your G arpeggio and G scale I suggest you play the scale and arpeggio slowly twice in the morning and twice in the evening. The next day take it a little quicker, but only as fast as you know you can do it without mistakes (even if that is taking it 2 seconds per note).
Practicing it any more than that and making mistakes will only teach you to do it the wrong way. So,do it slowly, decisively, twice in the morning and twice in the evening.
Answer to Q2: You get really sweaty and nervous in front of your teacher probably because you are insecure about something. Try to understand and realize she is there to help you learn more about the violin. You are probably afraid to make a mistake; but this is the perfect time to make the mistake - because she can fix it. Try asking her when you make a mistake if she knows why people make that kind of mistake. Trying being prepare at your lessons, if you didn't have time to practice tell her that you didn't practice very much this week and ask if she will walk you through how to practice this piece correctly.
Not enough teachers ever teach their students how to practice. If they do they seldom do it more than once, yet they have students practice scales constantly. I do review how to practice with my students. And I always ask them how much they practiced this week - not to make them feel bad, but because most of them are very busy and if I know how much they did or didn't practice then I know what to expect and then I can help them practice the piece, etude, or whatever and learn something from the lesson.
Another thing on getting nervous. Music is an enjoyable activity. People you play for love to listen even if you're not Izak Pearlman. They really do and that don't worry about a little mistake here and there. So, relax and enjoy when you play. Try not to over think things. Meditate a little before hand - breathe slowly through your nose (really slowly) until you are only thinking about your breathing and you are relaxed and calm - then play and be happy and joyous about it.
Answer to Q3: Tuning. Practice - on violin this is a long time project. We generally go sharp after we start playing because our arms get tired and fatigued very quickly causing our elbow to drop down and pull back towards the body resulting in the hand moving up on the finger board. You need to develop strength in your left arm and learn consistency. This is learned by repetitiveness. Get a tuner and make sure you start on pitch. Then check it every staff to get you to keep your left hand in position on the finger board.
Answer to Q4: Do I think you are doing well? If you have been playing for 10 years I would have some concerns. If you have been playing only 1 year I think you are doing fine. The most important question is do you like, or are you going to like playing the violin. If this is simething you want to do then by all means keep it up and enjoy what you are doing.All these problems are easily corrected.
Quote from Ronny Romm (Canadian Brass founder and trumpet player extraordinaire). "We are all fantastic musicians. Some of us just aren't there . . . .yet."
It's not meant to be easy, but the challenges are emant to be fun.