The metal washer does NOT go inside the tank.
If you have a set where for each bolt there is one rubber washer, one metal washer and a nut, then the order is bolt head in tank, rubber washer under bolt head in tank, then the metal washer and nut go under the bowl.
See diagram 3B HERE
If you have a set where for each bolt there are two rubber washers, two metal washers and two nuts, then the order is: Bolt head and rubber washer in tank, metal washer and nut on outside of tank, then, under the bowl, rubber washer, metal washer, nut. See Korky diagram 6A HERE, for example. Or Fluidmaster instructions: HERE
Toto gives you two metal washers and only one rubber washer; they don't have you put a rubber washer under the bowl. See illustration 4 on page 5 HEREfor how to do the inside of the tank, and the text of the second paragraph of instruction 5 as to how to do the under-the-bowl.
As to your second question, the rubber washer (assuming you have two per bolt) goes under the bowl. See diagram 6A above.
Lots of handymen (and, apparently, aprons) think that you put that metal washer under the bolt head. Do that, and you are reducing the seal between the bolt head and the rubber washer, with which the bolt head should be making a watertight seal, and reducing the ability of the bolt head to seat the rubber washer against the tank. Hence, you are increasing the chance of a leak.
Bottom line, you have metal against metal underwater in a place you are trying to have a watertight seal. On the face of it, that's obviously wrong.
There is no rational reason to put the metal washer inside the bowl. I think the myth arose because dummies bought bolt sets without knowing how to do the installation, and just guessed at where stuff was supposed to go; then they showed others how to do it the same, wrong, way, and that's how many people have learned to do it. But it's irrational and totally-wrong.
Now, under the bowl, it's a different story. There, you have a nut, and you are using the nut to compress the metal washer against the rubber washer against the bowl.
By the way, the consensus on the forum is that a good-quality set that has two nuts, two metal washers, and two rubber washers per bolt gives an installation that is the least likely to leak. The idea is to make the seal between the bolt head and tank first, using the nut and metal washer. Now you have a bolt coming nice and straight out of the tank, held in place, and a nice seal between the bolt head and tank, before you even start reattaching the tank. That straight bolt, held in place, is going to make it easier to properly-reattach the tank. Put another way, the attachment hardware has two missions: (1) make a waterproof seal and (2) hold the tank in place. The way we prefer to do it, you have a set of washers and nuts for each mission and you do each mission separately: i.e. make the seal and then reattach the tank. It's possible to use one metal washer and one nut to apply the tension necessary both to make the seal and also to secure the tank on the bowl, but your long-term success rate is likely to be enhanced by doing each job separately.
Of course you still have to tighten down the tank slowly and carefully, keeping it vertical and alternating side-to-side (i.e. tighten a little on the one side, then a little on the other, so it stays basically straight as you are pulling it down to meet the bowl). Stop the moment you have any china contact against china, because one more turn and you will likely crack it. When you stop tightening, examine whether the points of contact are correct. If not, loosen, straighten and try tightening again. You should have no wobble of movement in the tank, but only a whiff of contact between china pieces.
If you want a good giggle, here's a thread on this from Dimwit City: BAD ADVICE Another good reason to hire a plumber not a handyman. (Or do it yourself with the excellent, professional advice that real plumbers Terry, HJ, Jimbo and others give here.)