What was a proposed alternative to Segwit?
The alternative was to incerease block size to 2MB, thus allowing storage of more TXs.
What did Segwit solve more than just the scaling issue?
It also solved the possibility of modifying the has of the transaction. ( transaction malleability.)
How is Segwit and the Lightning network connected?
Lightning is a second layer protocol, and Segwit supports it.
Are people, wallets and other services forced to use Segwit?
No they are not forced to use it, thus the implementation is quite slow.