You're right about Sentence 2:
(2)This is roughly as much as the country spends on defense, foreign aid, higher education and research put together.
The pronoun "this" obviously refers to a certain amount of money that has just been mentioned, and therefore there's no need for another pronoun to represent it. It's not wrong to use "what," but it's not necessary.
(1)The sick can claim 80 percent of their wage up to a certain level, at an annual cost to the taxpayer of about 105 billion kroner($15billion).
...seems to be about claiming sick pay from one's employer or from the government while one is sick and unable to work.
Workers who earn a regular income below a certain amount, or level, can claim up to 80 percent of their regular income while they are sick or otherwise unable to work. Workers who usually earn an amount greater than that can claim a smaller percentage of their regular income.
The word order of the two final prepositional phrases is as it is for a reason: to put the newest, or the more important of the two pieces of information, at the end of the utterance. The "end position" is the "strong" position. The information about the amount of money the taxpayer has to pay is more important than the information about "the taxpayer."
If the order were changed to have the phrase "to the taxpayer" at the end, it would make the amount of money less important. The original word order is the better one.