What was a proposed alternative to Segwit?
Increasing the block size an the alternative to Segwit. This lead to the creation
of Bitcoin Cash
What did Segwit solve more than just the scaling issue?
Yes, it fixed a bug called transaction malleability that allowed someone to change small details which then modified the transaction Id, and the hash.
How is Segwit and the Lightning network connected?
The malleability fix allows second layer protocols like the Lightning Network. The fix allowed easier designs for features that rely of unconfirmed transactions since the transaction Id can not longer be changed. The Lightning Network would not be possible;e without this change for Bitcoin
Are people, wallets and other services forced to use Segwit?
No some wallets have yet to add Segwit support. At this time 40% of Bitcoin transaction use the Segwit fix