2. Nodes don't need to continue to do hashing once their transaction is accepted, others will do that for them if the majority confirms those transactions that confirm others' ones.
Still I can't see why nodes would try to put more PoW into their transactions. Looks like it is enough to submit minimal PoW and have others confirm my transaction with their PoW. It is in the common interest of all users to have more PoW on the legit branch to secure the network against doublespends, but individual interest, it seems, is not aligned with the common one.
3. If a transaction happens to reference double-spending transactions then anyone can change the references.
I hope the change is deterministic? Otherwise we'll end up having many conflicting "fixes" of references.
Every transaction has 2 parts - essential data signed by the owner and references to other transactions, - the latter can be changed without transaction resigning.
This raises another concern. What if a malicious node changes references of a third-party transaction before forwarding it to peers? Different nodes will receive different versions of the same transaction that differ only in references to parents. Also, if references are not secured by signatures, nor by anything else, is it possible to reorder and even censor old transactions, thus changing the graph structure?