Honestly, it sounds like you are doing great! The fact that you recognize these issues that you're having is a big thing in and of itself, and you seem very conscientious and thoughtful. ALL of this gets easier with time and practice. It's really okay with the opening the meds thing - it's like they specifically make certain packets to be impenetrable. Don't feel bad about repeating little mistakes a few times. It took me at least a couple of months to learn how to hang IVs without the tubing looking like a damn pretzel. Especially when it comes to dexterity, it WILL improve the more time you spend using different strategies.
For remembering all the meds to give, it might help to just do a quick inventory of what is due at that time and what you have gotten before you enter the patient's room. I do a quick double check over everything after I've done my five rights and whatnot. This also helps you make sure you've got whatever supplies you need (e.g., multiple flushes, syringes, blunts, water cup), and you can verify whether you need more than one pull to make a full dose; sometimes you may need to split a pill. It seems like this might take a lot of time, but it will save you much more in the long run.
Totally agree with whoever said not to take your preceptor's alleged annoyance too personally. As a newly minted preceptor, I have caught myself being impatient a couple times, and then I think to myself, "You were dealing with the same challenges a year ago!" We are all new and awkward and forgetful ay some point; lots of us just prefer to forget.
Don't pay it any mind when you start to perceive those reactions. This is your time to learn and to be cautious and develop your skills and critical thinking. No one else's attitude should interfere with that.
Finally, as far as the fall risk thing, make it a habit to round on your patients as soon as you finish report. "Hello, I'm CaseyKay, I'll be your nurse tonight. Is there anything you need right now? I'll be back soon with your medicines for the evening." *Look at bed alarm, look for non-skid socks, etc.* Make it part of the very first interaction with your patients, and it should soon be an instinct every time you go in the room.
You are doing just fine! Keep learning, and keep up the good work. You will be great.