Learn English – Using “on” with “the day (on) which…”

At the in-orbit acceptance date of the satellite, the facility was fully drawn[,] with USD 152.2 million which will be repaid in 17 equal semi-annual installments starting on June 22, 2012.

So (as I think you know) a credit facility is a loan or collection of loans made to a business entity. As near as I can tell, "fully drawn" is used in finance in the senses of definitions 65 and 66 here, as in to call upon the resources of something. So a fully drawn loan is one that's been entirely paid out to the borrower.

So I would read the quoted sentence as though it had the comma in brackets. "With" then means "having"--the loan is fully taken out and has a balance of 152.2 million USD to be repaid under the stated terms. I could see substituting "having," which is both not a preposition and less idiomatic than "with." Otherwise, "with" is the preposition we use to provide supplemental quantitative information: compare the phrases "with an error term of..." or "with estimates exceeding..." I do not believe any other preposition would serve this purpose.

On these four series, the Group pays interest semi-annually.

"On" is used here because, as others have stated, that's the idiomatic phrase to refer to payment of interest related to a particular borrowing. I suspect, but can't demonstrate, that this is at least in part because interest is a mathematical context relating to some basis; we frequently use "on" to compare a part to a whole when the basis of the comparison is important. As an example, "An error of 3 cm on a total measurement of 15 m," or the titles of this paper or this paper.

Because the sentence is inverted, I would accept "For" or "With" in this location; however, I would expect the context to be making a distinction between the payment terms of these series vs. terms of other series under discussion. For example, I would find it acceptable to say "For these four series, the Group pays interest semi-annually, while for the majority of its borrowings, interest is paid on a monthly basis". Without that comparative context, "on" is the better choice because of the idiom of paying interest on a loan. I would not in any case accept "*The group pays interest with these four series semi-annually"--the inversion is required for the comparative context to make sense, and "with" or "for" are not idiomatically appropriate for discussing interest.

The Macmillan Dictionary blog has a nice article about "bored with" vs. "bored of". The conclusion is that they are interchangeable, with the latter being considered a newer usage in the language (also corroborated by other comparisons between the two you can find online, such as this one). The Cambridge Dictionary's entry for bored shows examples with both "with" and "of", as well as an example of where it's OK to drop the preposition altogether.

"bored by" seems to be another equivalent way of saying the same thing. It seems like it was a popular choice in the past on par with "bored with". It's still not unpopular today - take a look at all these examples from printed books. Personally, I'd use it when I want to emphasize the feeling of boredom, rather than that something is boring, but I can't claim that's a general rule:

I'm bored by this presentation. (= This presentation makes me feel bored).

I'm bored of/with this presentation. (= This presentation seems boring to me.)

"bored from" means "bored as a result of", as you can see in the comments section of this Bored Panda (ahem) article. So you wouldn't typically say "I'm bored from you" (= bored as a result of you ??). I suggest looking it up in Google Books as well to get additional examples of how it's used.