trust me that you are increasing your risk of being denied citizenship if you apply or even may be be revoked from your asylum.
1. But its still possible to go back but a problem is that if re-entering the US ,at the aiirport they will place have to ask you where you went to and which country was your country of persecution ,all i can tell you is that you say ,your truth because you cannot lie them.I understand you that your grandma is ill and for anyone he will want to do the same as you ,but what you need to also understand is that you will just be playing with a lot of risks of not entering back,so that's what you need to first know.
2.no the best way to travel back is when you are a US citizen ,because at that time the US is able to take responsibilities if something happens to you in COP and as a citizen ,you have all the rights just as a newly born citizen.So if you can wait and be a citizen ,then fine.
3.yep ,this is definitely where all your travel records will come up ,because they will study all your trips ,your background and many other things ,i haven't applied for it but i have read a lot of procedures they do ,but i bet you that this will be that final step and they wont let anything pass off their eyes.
Please i understand that you grandma is really sick but you will also be playing with your life by going back home ,but as a friend ,i will tell you to do what your heart really wants to do and remember that if you want to re-enter the US ,i will advice you to have a lot of proofs that will show everything you went to do over there and pls dont stay for long ,sometimes the immigration will live you re-enter from what i heard but provided you have very powerfull and sufficient reasons .Good luck