English Tense

I can't imagine it's (don't forget the apostrophe) so efficient, it takes (with an s) no more than 24 hours to place an order, despatch (why don't you use dispatch) and arrive at your doorstep.

OR

I can't imagine it's so efficient, from placing an order, to being dispatched till arriving at your doorstep, it takes no more than 24 hours

You can use either one, they both work, just phrased a little differently

btw: despatch is a variant of dispatch, meaning a modification, an alter, I would suggest the use of dispatch, but if the use of despatch is required, then go ahead using it.

Good !

全錯，因為 that it take 應是 takes

第二句較為正確
being despached 是被動式，till it arriving 是一定錯的，因為till 之後應用present simple tense