When wearing the bag for extended periods of time (like when sightseeing) does the strap dig into your neck?

I have been traveling with my bag this summer and it has worked perfectly. The strap is wide enough that it stays where I put it for crossbody and I have not had any problem. I usually set it back towards my shoulder and it stays there. I do not overstuff the bag and really can forget that it is there. I love being able to adjust the strap for over the shoulder or even shorter for the elbow depending on what I am doing. I have other crossbody bags that did dig in and were constantly slipping off my shoulder when wearing them. This one hasn't been a problem and it is my second one purchased I got my newest one in the light color for summer, My other is black. Must be good when you want it again!

Would this fit a standard (16.9 fl oz) plastic water bottle standing up and be able to be zipped closed?

No. But if u put the bottle at one of the bag standing up u could close the zipper up to the bottle cap. This was not my favorite purse. The material makes it heavy.. I must havev 8 battalinis and this Is my least favorite. Get one in nylon my iPad insists on changing the spelling to its own version of the word I want. I apologize for that.

Is the bag rfid or just the accompanying wristlet?

Just the accompanying wristlet is. I love those purse and would purchase again.

Does this bag have a cell phone pocket?

Yes, there's a nice pocket in back with a side zip that I think was the intended phone pocket. It might work fine for most phones. However - and this is just my observation only, if you have the extra large IPhone, the phone pocket will fit the phone without a plastic protector, but will not fit comfortably with a plastic protector on the phone. My solution was to keep the plastic protector and make a nice slide on cover from fabric remnants for the main purse pocket. I just toured DC with this purse for 4 days and found it extremely useful, in fact I loved it everywhere I went. It especially works great when you are moving through security checks which are performed in every single museum! You just open all the pockets, they take a quick look, and you're ready to move on. Fantastic travel purse.