1. There is a mining requirement because transactions sent without proof-of-work mining share would form a rejected block, thus will not be accepted by any block.
2. The sender of the transaction doesn't need to win a block to send a transaction. I claim a 51% attack is impossible in my design. The specifics on how I accomplish that protection is not going to be discussed now. It hinges on objectivity which Satoshi's design doesn't have. Sincerely I feel bad for not being able to discuss the specifics on that now (I am eager to of course, because I am proud of my design even if it is not perfect because nothing is perfect) but please do not drag me into another argument because that particular feature is my intellectual property. I am trying to accelerate my coding so I can get the white paper and code released into the open source asap so we can open discussion on the specifics.
For 1, I was more asking why a miner would be incentivised to mine a chain with no block reward.
I can see how a 51% would be impossible in a system where only you can mine your transactions, but it looks like this is not your design. In the system I was musing about, the 51% attack was replaced with the attacker only having to outpace the recipient of the transaction, which is much worse than only having to outpace the network.