Dunno if you will get notified, but I will still reply!
1. From a functional perspective, there is no difference, since they both achieve the same goal, which is a longer focal length (or zoom). The difference is in the hardware. Normal telephoto lenses behave essentially in the same way as a normal 24mm lens on the primary camera.
Periscope telephotos came because of two things, longer zoom ranges (like 5x) and bigger camera sensors that also come with a much smaller crop factor compared to the Full Frame Equivalent. Take the Oppo Find X6 Pro (and X7 Ultra since they share the 2.8x module), the periscope is HUGE! Not to mention very thick, no wonder why Oppo had to use a giant camera bump. Meanwhile compare to Samsung which has the 3x module in a very small housing on the S21/S22/S23/S24 Ultra.
That is because of the sensor sizes. Samsung uses a Sony IMX754 sensor with a 1/3.52" size, whereas Oppo uses the much superior IMX890 with a 1/1.56" size. While the sensor used in the Oppo phone is a million times more superior to the one used by Samsung, this comes at the cost of making a much more complex lens, due to the much smaller crop factor in the Full Frame Equivalent, which is why the module is so huge on the X6 Pro/X7 Ultra.
As for 2, it's actually both Engineering reasons and Marketing reasons.
Having small phones with longer focal lengths like say 120mm is pretty difficult. For one, they need a lot of space, especially if they use superior sensors that are big. Secondly heat also becomes a problem, since they generate quite a lot of heat (both the sensor and the OIS or Sensor Shift mechanism), and this becomes a problem for the cooling systems of the smaller phones.
The Engineering reasoning is very much valid... which is also a great way for the Marketing side of the project to make it an upselling point to the higher-end models.
Hope this clarifies things!