1) Are MX Reds just Browns but without the tactile bump? Or is there any other differences to note?
Different people would answer this in different ways. I would say yes, they are similar but with a tactile bump. But it is not "just" a tactile bump. To me, this changes the feel and characteristics of the key considerably. So even if that is the main difference, it is not an insignificant one.
2) Has anyone experienced the same problem with Browns being "too light" like the Reds?
They do have the same actuation force, but if I had not read about this fact, I would have sworn browns felt heavier. It is because it is not a linear switch and the tactile bump brings some variation in the resistance as you press the switch. This also made it much easier for me not to have any accidental keypresses. The reds are easier to press accidentally because there is nothing "warning" you about the point of actuation. With browns, I do not press the key past the tactile bump unless I intend to. It is kind of hard to describe because it is not really a conscious process, it is just the way your fingers respond to the feel of the key.
3) Since I don't have this problem with Browns, will Reds not be a problem either? Or are Reds really that much different than browns?
There is not guarantee. I had that problems with reds. And it is not like I tried them for a day and decided I do not like them. I tried reds before I ever used browns, and used a keyboard with reds intensively for about a year. Even though I loved the feel of them, accidental keypresses remained an issue for me. Getting browns solved this problem pretty much completely. Though that does not mean that you would experience the same thing. I think the two switches are considerable different however.
4) Which of the two do you use (if you do), and why? What are some other advantages/disadvantages that I should consider between these two switches?
I use browns, but can really see the appeal of reds. Honestly, if I could not use browns and had to stick to reds I would still be pretty happy. I do not think there are clear advantages or disadvantages to using either one, for gaming or typing, I think it comes down to preference. One thing I will say though is that is seems possible for me not to bottom out on browns ( even though I do not do it consistently), not bottoming out on reds felt completely impossible for me, even though I am sure there are typing ninjas that manage to do so.