Yes, legends are what you see on the cap, whether that be the letters or any symbols. They can be "printed" in numerous ways. If you're looking through various group buys, the one you'll probably see most is doubleshot, which is one shot of plastic for the legend, then another for the rest of the cap. You may see dyesub, which is a process where the legend is dyed into the cap. Then there is pad printing which is just as it sounds, laser etching which is as it sounds, and various other techniques. These are generally considered less desirable than the first two. Each one has disadvantages and limitations.
Modifier sizes are based on the size of a single alphanumeric cap, which is 1x. So a 1.25x mod is a quarter of a cap bigger. Generally, that is based on the keyboard you're using. A Filco or QFR will have a 6.25x spacebar with 7 1.25x mods. A Korean keyboard or certain Cherry boards or most older IBM buckling spring boards use a 7x spacebar and 4 1.5x mods, some also may have 1x mods in between Ctrl and Alt. Generally, they all add up to 15x across the row.
R1 or R4 related to the round, or number of times that set has been ran in relation to a certain set. If you only see R1 or R4, someone is probably discussing a series of GBs (group buys) ran by 7bit, which are very large, time consuming, and offer many different choices.
In regard to profiles, the word is used generously. If you're discussing the shape of the cap, we usually discuss DSA which is a spherical shape, while most others are cylindrical, called DCS. Note that those two names are used by SP (Signature Plastics). Generally, all other caps are cylindrical unless it is mentioned they're spherical or something else. So the stock caps on your keyboard will be cylindrical.
Height profiles are generally one of the three you mentioned. OEM are the tallest in height. SP is Signature Plastics DCS height profile. It is lower than OEM, close to Cherry with some differences from it, the most prominent being the deeper slant on the two bottom rows. Cherry is Cherry's profile height. People use SP caps with Cherry sets due to the similarity. Each row has different heights within each profile, so the top rows are higher than the middle, which is higher than the bottom. If someone is discussing DSA, you should note that they are all the same height.
POM is a type of plastic, as are ABS and PBT. Generally, ABS caps are doubleshot per above, while PBT caps are dyesubbed. POM caps are usually laser etched or printed or pad printed. You can usually laser or pad printed any of the plastics. Recently, we've seen some doubleshot PBT caps which hasn't really been done before. It offers the resistance to shine PBT offers while offering the color ways that we generally see in doubleshot ABS, so people are excited for the possibilities but they currently aren't on full offer.
Those are what I was talking about in regard to the rows being higher than one another. Differently companies call them by different names, so its hard to pin down, but generally the top two rows are the tallest and usually the same height as each other, the next row down (QWER) is shorter, the one after that a bit shorter (ASDF) and the bottom two rows (ZXCV and mods) are the shortest. The bottom two are generally the same height, but some sets have the most bottom row a different profile. Usually those are seen in Cherry sets, where the normal (by today's standards) is called B while the older ones with a higher slant are called A.
Height doesn't affect compatibility. Some people just prefer one over the other. People who prefer OEM height seem to be the minority, but they exist. Generally, people prefer Cherry and settle for SP.
The height of caps in arrow clusters and such is based on the row they're in. Arrows are on the bottom two rows, so are the shortest height, and are usually the same height as each other.
