In terms of something fitting in the sense of physically attaching to the bike, I don't think you have much to worry about. In fact, for the stem and bars, you may not even want an exact match to what you've got already, as playing around with those can be a great way to customize the feeling, handling, and comfort of the bike.
Where the stem attaches to the steerer tube should be a very standard 1 1/8" and is often not even specified on product pages. On the other side of the stem, you just need the diameters of the stem and bars to match, so a 31.8mm stem with 31.8mm bars for example. If you replace both together, you can choose whatever size you want as long as they're the same. They'll both also have various angles to them (on the bars they may be referred to as upsweep and backsweep), the bars will have a width and rise, and the stem will have a length. While all these numbers will change the ride feel of the bike in various small ways, they don't factor into compatibility. Normally these numbers should all be printed somewhere on the components themselves, but otherwise you can always just take a ruler/caliper and/or protractor and measure them directly.
For the tires, the product page says they're 700x40c, which like the other components should be stamped on the sidewall somewhere. You might also see something like 40-622 which is the ISO/ETRTO equivalent of the sizing. This means the tires are nominally 40mm wide, the bead of the tire meets the rim at a diameter of 622mm, and the overall diameter of the whole wheel including the tires is approximately (but almost guaranteed to not actually be) 700mm. Buying by the ETRTO size is the best way to ensure a match. You have some wiggle room in the width, you'd probably be just as fine if the width were 35 or 45, but the 622 number is an absolute requirement. If all you can find is marked only by 700, make sure it is 700C and not 700A or 700B, the other letters won't work, only C.
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