First off your little lady needs a ratty friend. Whilst humans can be fun, they don’t give them the company that they need. We can only be there so much of the day and ultimately don’t speak rat very well. A similar aged little girl (top eared or dumbo) would really make her life better.
In terms of training her, she sounds like a typical baby, full of energy and wanting to explore, I would give it a few more weeks of just spending time with her and building a bond before going fully into training. She is likely to have better concentration in a month or so. Then start simply, the first thing to teach is recall. My guys don’t have food in there cage all the time, instead they get fed twice a day. I play with them before the evening feed and to get them back in I train them to hear the rattle of the food tub and head back to the cage (mini stampede), you can do the same with a word, there names or similar, but it only really works well if you limit there food.
For further training you need to find something she really loves, this doesn’t have to be a food treat (though little bits of chicken or seed are high reward), some rats love a scritch, cuddle or just being praised.
In terms of rat harnesses, I would say there not much good in general. I’ve only found one design that actually is reasonably secure (kind of looped figure of 8 style) and even then it only fits big bucks well. Most rats can get out with no effort at all (just back out of it) and some rats get very stressed by it. If your planning on trying it I would leave it until she’s a good deal bigger (say 6 months old) then try putting it on her without attaching the lead, treat her once you have and let her wander around with it for a bit. If she gets distressed take it off, though washing is normal. After a few times she should be starting to get used to it so try attaching the lead. I’ll be honest even with the big bucks I’ve had that quite liked it its more a case of the rat leading you and if they really tried they could get out. You use them to let the rat wander somewhere that’s not 100% safe (say a none rat proofed room) and gentley guide them away from the areas that they aren’t allowed. If they get determined though you’ll need to pick them up and move them elsewhere as the lead wont stop a determined rat.
To be honest your better spending your time training them in recall and setting up a rat safe place for them to play, in the 30 ish years I’ve had rats I’ve had maybe 2-3 rats that would tolerate them well and seemed to enjoy the freedom whilst not getting frustrated when I wouldn’t let them go somewhere, and they were all bucks, does are much more stubborn lol.
