>1. Can blockchain-based currencies really work with billions of users?
No, they do barely work now.
>2. Will it become a choice between impractically expensive fees or impractically slow transaction confirmations?
Both has happened already.
>3. Are the proposed plans for BTC and ETH scalability just short-term fixes that will eventually run into the same problems later on?
Aye. At first they will increase block sizes. They may also reduce block time. But at some point network propagation will be a big problem.
The new buzzword is "Lighting Networks". This is why Litecoin was pumped to over 2 billion. Lighting networks means the introduction of banks as a part of a blockchain. The customers of a lighting bank, or lighting network as they call them, will be able to instantly exchange tokens with another customer of that bank. Just the same way like transfering BTC within the same BTC exchange. The bank will then at a later time generate blockchain TX if necessary.
>4. Are DAGs the solution?
To an extent. They can replace blockchains, but have their own problems.
>5. How much time will IOTA transactions take if each user has to process their own share of the "tangle"?
That depends on the number of users in the network. Fast transaction are only possible when there is a lot of activity in the DAG.
>Can tiny IOT devices even handle such processing requirements?
Currently they can't. From IOTA #tanglemath channel I've received an answer similar to this:
Tiny IOT devices like temperature sensors will connect to a proxy node and send the data. The proxy node will take the data and create a TX by doing the POW.
At a later time the sensors will be able to generate the POW themselves by using the JINN processor. This will be a trinary processor with extremely low power usage. Apparently they work since 2 years on that hardware, with CFB/BCNext as the chief architect.
>6. Others have suggested that currencies such as DCR, PIVX or BURST solve the problem in different ways. If so, how?
From these 3 I know only PIVX, which is Proof of Stake. It's nothing new, basically a copy of NXT with some modifications. POS coins have way faster TX time than blockchains, but they suffer from centralization.
>7. Are there any other solutions?
I'm biased about this, but the only endgame solution, meaning one that will still work without problems 30 years from now is Radix. You will see it in action soon.