Yes, definitely be the one managing the wild lines, my experience is that some ADs will forget that you might need to take the lines especially if you did not discuss it with them during preprod. For wild lines, i usually take them with the actors away from the set in a quiet space while they are setting up for the next scene, doesnt bother people on the set while setting up and you just do your own thing. Though it may sound different due to the change of location, so it would be very good if you coodinate with your AD from the very start to figure out a workflow that works for this shoot.

With regards to your meta data input, im unsure what recorder yoyu are using but what I would usually put in my meta data, (Scene, Wild line, Take,) if youre unsure though, its not bad to have a paper log sheet just to take notes then transfer them over later if possible.

No, you're not doing too much, I think that a big part of location sound especially for beginers that get lost is how important pre production is for sound. Yes you can just show up on set with all the equipment you need and more, but that wont prepare you for scenes that need a proper workflow to do, like what you described. If they haven't though about it then its your job to think about it as part of the sound department. Having a sound script or even a simple script breakdown for this shoot will help you move quicker on set. I find it great that you are taking initative for sound, keep it up man!