A) Why make them separate?
Long-term, only ARDR transactions are stored forever in the blockchain. Child-chain transactions (IGNIS, Bitswift and others) will be pruned. That helps keeping database (blockchain) size low. That is also the reason why IGNIS transactions cost 100 times less minimum fee than ARDR transactions.
You should really memorize that, because it's Ardor's main innovation and until to date one of the best scaling solutions. An example: If Ignis had the same transaction volume than Bitcoin, it's database would be about 30 times smaller (for full nodes).
B) What is the block time on Ardor and Ignis.
60 seconds.
C) Has one of them have smart contracts?
No, Ardor's stance here is similar to Bitcoin's. However, some useful smart-contract-like features are hard-coded ("Smart transactions").
E) Can you send cross-chain transactions?
You can trade one child chain to another and to ARDR on the blockchain ("DEX" way). Is that what you mean?
F) Can you sync one of them or do you need to keep getting blocks from both chains?
After pruning has started, all full nodes will sync and validate, by default, only the Ardor chain and the last 1440 blocks (roughly one day) from all child chains. You can, however, choose to be a "archival node" for one or several child chains and sync/validate/store all blocks.
Until pruning has started, all nodes sync all child chains, afaik.
