You can run the idea by an attending and then go for it if you feel like you can handle it by yourself. In general though, unless you're some hotshot bigwig researcher I think there is commonly some bias against publications with a single author, much less a PGY-2. It's so easy to add names to the publication, so I would recommend that you still find an attending who is willing to sign on to your project and look over it.
And this gets to a point that I forgot earlier: the point of having a mentor is often so that you know how to ask the right questions. These attendings have been in practice and going to specialty-specific conferences way longer than you have, and know the hot topics and nuances of the field immensely better than you. Some attendings are literally gold mines for ideas but due to their age, clinical commitment, or lack of analytical/stat skills cannot carry out research projects themselves. I had some of my greatest success working with these older attendings who gave me great ideas for projects and allowed me to run with it (and obviously I am happy and grateful to include them as the PI as they came up with the original idea). This applies to any type of research, whether it be a case report, a lit review, or a prospective trial. Sure, anyone can go on Pubmed and see if some idea has been done before, but is it relevant to the ongoing discussion in the field?
For your second question, no there is no easy way. The most robust and structured way would be to tag on to a MSc/MPH program at your institution (likely after you graduate or start in your 3rd year if they have classes that don't conflict with your scheduled work -- I personally do have a masters that I did in medical school). You can learn by apprenticeship in residency by asking statisticians good questions and reading up on stats yourself (UCLA IDRE is an amazing website). There are many intro-level stat texts for clinical researchers and you can work your way through one of them to get a better understanding. Honestly, the biggest thing in stats is knowing what analyses to run and the assumptions associated with these analyses, which is both easy and hard to learn. Hard because if you don't know what you're supposed to learn, then you just never know unless someone tells you -- but easy too because once you know, you can do 80% of common analyses in medical literature solo without too much statistician oversight. I do all of my own analyses for my papers but I do run the final results by a statistician who then tweaks my analyses a bit to take into account certain assumptions...etc. or adjusts them to another, more obscure, model that might be more appropriate. Learning stats is kind of like snowboarding. It's really hard to pick up in the beginning, but once you have a firm base, the learning curve isn't incredibly steep for the purposes of medical research (I am always shocked at how little general attendings/clinicians know about stats even though everyone tries to pretend at journal club).
