I really wonder whether the new blockchain works as intended.

I do not get the part that each transaction requires the sender to verify two other transactions on the Tangle.

Does this means that a sender is always dependent on future senders to get his payment confirmed (checked and verified by those future senders)?

If so, in theory the system could encounter a problem if 10,000 senders make a payment and thereafter, only 1 person makes a payment each day. It would take a long time before that sender has verified all 10,000 payments before that. And of no one makes a payment for a long time, all the latest payments (still unverified) would remain unconfirmed.

Am I missing something?