It surely does good, it's a solution for the block size limit,
Segwit makes use of weight to reduce transaction fee.
Possibly because of the vbytes metric, it is a common misconception that segwit somehow makes transactions much smaller—but this is incorrect. A 300-byte transaction is 300 bytes on-disk and over-the-wire. Segwit just counts those bytes differently toward the maximum block size of 4M weight units.
The maximum size of a block in bytes is nearly equal in number to the maximum amount of block weight units, so 4M weight units allows a block of almost 4M bytes (4MB). This is not a somehow "made-up" size; the maximum block size is really almost 4MB on-disk and over-the-wire. However, this maximum can only be reached if the block is full of very weirdly-formatted transactions, so it should not usually be seen.
The typical size of a block depends on the make-up of transactions in that block. As of 2017, the average transaction make-up would lead to blocks with 4M weight units being about 2.3MB in size if all transactions were segwit transactions.
In wikipedia it says that SegWit was activated on block 477120, but who begun that?
I do not know much about consensus, experienced members about it will answer that. But what I know is that segwit transaction begins with miners supporting it activation, while majority supported it and makes the activation successful.
Public key to private key reversal. (I've heard that it may be possible to do that with quantum computing and pollards kangaroo method)
Private key can not be reversed as it is a one way function. But you meant can it be brute forced through the use of quantum computing. According to what I learned, it is not early days quantum computers that can brute force the ECDSA, it will take time before this can happen, and before it will happen, there would have being layers of protection against quantum computing to brute-force bitcoin private key from public key.
Finding collisions for RIPEMD-160 hashes. Are we sure that 2160 is strong enough? What if it becomes weak in the next 20-30 years?
Double hash/hash160 is used in a one-way-function to generate addresses from public key, it will be much harder for quantum computing to brute force private key from addresses. And know if this is becoming possible, there will be another layer added that will be impossible for quantum computing not to brute force the private key.