Very nice progress for 2 weeks, congrats.
Your rhythm is a little off for the bottom deal, very noticeable on the first deal. Also try not to tilt your left hand so much on each deal, keep it still as much as possible.
Keep it simple like hiding it in your sleeve and pulling it out. It can look very nice if you practice a bit in front of the mirror.
Even if you mess it up from getting nervous or whatever, it will still be cute and fun probably get a laugh.
Yeah there are heaps of them. Look up sleight of hand in a good classic magic book like Bobo's modern coin magic, it will keep you busy for a long time. The book is in the public domain so you can probably find a free version floating around online somewhere.
Do a google search of some hospitals/organisations near you. A lot of them will have a page on how you can contact them to volunteer. In my opinion it is not really that important exactly what tricks you perform, just anything you feel comfortable with and can do well.
Yeah pretty much just practice as much as you can. Practice in front of people if you can, like friends and family.
It will give you a lot of confidence once you have completely mastered your act. It will help reducing nervousness on stage too.
How did you injure it? Is it a sprain? If it is you can try some stretching exercises here, it will usually take 4-6 weeks to heal completely
https://myhealth.alberta.ca/Health/aftercareinformation/pages/conditions.aspx?hwid=bo1531