Can people still make normal Legacy transactions when the Lightning Network is implemented OR do they have to make all transactions on the SegWit addresses?
Both legacy transactions and SegWit transactions that do not involve the Lightning Network will still be possible. Lightning Network runs on top of Bitcoin, the Bitcoin protocol itself doesn't change.
Can people spam the Blockchain with old Legacy transactions and then cripple the Lightning Network too?
Spammers can only affect the on-chain transactions that are required for opening and closing a channel. The routing on Lightning Network itself won't be affected by on-chain spam. Depending on its implementation there may be other ways for an adversary to affect LN performance, but that's too soon to tell. One can assume that spamming the network will become less effective as more transactions are moved off-chain and lightning channels are kept open for prolonged durations of time.
