Is that what you wanted? If not, perhaps you need to devote more thought.
I'm not sure where you get your quarter-million number from. Bitcoin before gets us 3 to 4 tx/s
3 tx/s
180 tx/m
10,800 tx/h
259,200 tx/d
x1.7x if everyone uses segwit for 100% of their on-chain tx
440,600 segwit tx/d
/2 for settling twice a day
220,300 max users supported.
Show me a block representing 4 or more tx/s?
Segwit might increase block size greater than 1.7x under aberrational circumstances - but these circumstances include very large # inputs & outputs per tx. Still capped at 1.7x tx.
Your plan to double block size is a pig in a poke. Even allowing, the number of users supported is under a half million. Sound like a world beater to you?
See above analysis.
Yes, but if each user is to open and close a channel daily (your hypothetical, remember), Bitcoin Segwit can only support a quarter-million users. Even if I spot you the unobtainable number of 4 million, the only way you can hit a trillion tx/d is if each of your 4 million users initiates 1 million tx/d. I don't think there is a human alive that could generate that many transactions. Hell a preprogrammed Raspberry Pi cannot generate that many transactions in a day. A decent-spec consumer computer could. If it worked on it 'round the clock.
While this is true, you still have an insurmountable obstacle in the (1 open + 1 close per day) * number of users <= daily on-chain tx capacity.