Learn English – the difference between “work in” an organisation and “work with”

In the first sentence you've quoted, the phrase is not meant with but meant as.

With ‘new spirit’ the same must be meant as with ‘my spirit’ in clause e.

The with in "with 'my spirit'" parallels the with in "With 'new spirit'", as I've indicated in non-bold italics in the quotation above.
But, in fact, the as pairs with the same, as in "the same ... as".

I can't tell the full meaning without the preceding context, but it seems to be something like:

The use of ‘new spirit’ means the same as the use of ‘my spirit’ in clause e.

The second sentence is more difficult without more context.

The suggestion made by several commentators that the doom of Judea’s downfall is meant with the ‘first things’ that should no longer be remembered takes too little account of the poem’s own concentric structure.

I suggest it means:

Several commentators have suggested that the doom of Judea’s downfall is meant as [one of] the ‘first things’ that should no longer be remembered ... [or vice versa?]

But I also note that there is reference to a poem. It should be borne in mind that poems, songs, etc. often use 'strange' terminology for reasons of meter or rhyming.

In that sense, you can use 'by' with any tense. Consider its meaning as given by the Longman dictionary:

Before or not later than a particular time.

Examples:

• The document needs to be ready by next Friday.
• By the end of the day we had sold over 2000 tickets.
• By the time we got home we were tired and hungry.
• I'll be home by 9:30.
• Please try to have this done by Friday.

All the examples are borrowed from the Longman dict. so you can trust them.