1. What was a proposed alternative to Segwit?
A proposed alternative to Segwit was to increase the block size from 1 MB to 2 MB. However, this was not seen as a true solution but only a temporary one. With the increasing popularity and adoption of bitcoin, it would not be very long before the new 2 MB block size limit would be reached, placing the bitcoin network in the same situation all over again.
2. What did Segwit solve more than just the scaling issue?
Other than the scaling issue, Segwit introduced a fix for the transaction malleability problem. The transaction malleability problem would have to be fixed before any additional technologies (second-layer protocols, e.g., lighting netowrk, MAST, Schnorr signatures) could be built on top of bitcoin.
3. How is Segwit and the Lightning network connected?
See my answer to the above question. Segwith’s transaction malleability fix made any feature that relied on unconfirmed transactions less risky and easier to design.
4. Are people, wallets and other services forced to use Segwit?
No, people, wallets and other services are not forced to use Segwit. Segwit’s design retained the 1 MB block size limit, maintaining its compatibility with the previous protocol and avoiding any need of a hard fork.