Bad Translation attempt
「ブロッコリーは日本の人たちの生活に大切な野菜」
The heading appears to be pretty easy to translate this time (famous last words). I’d say it’s something like
“Broccoli is an important vegetable in the life of Japanese people”
Btw if you read this, is たち some sort of pluralizer?
国は、日本の人たちがよく食べていて、生活に特に大切な野菜を「指定野菜」にしています。
I’d say the first part is “In the country”. The second one might be “Japanese people eat well and…”. For the third, I think something like “the “Vegetable Assignment” (perhaps, this is the name of some sort of organization?) decides an especially important vegetable in the life.”
So, I’d go with something like this:
“In the country, the Japanese people eat well and the “Vegetable Assignment” decides on an especially important vegetable in life.”
__
今はキャベツ、だいこん、トマト、なす、ねぎ、たまねぎなど14の野菜があります。
This appears to me like a list of things, with the など indicating that this list is not complete. The things that are being listed are cabbage, daikon, tomatoes, eggplants, spring onions and (normal) onions. I’d say perhaps this could translate as something like this:
“Now, there are cabbage, daikons, tomatoes, eggplants, spring onions, onions 14 more vegetables.”
I’m quite unsure about the “14 more vegetables”, but it confuses me a bit that the 14 and 野菜 are linked with a の 
2026年からブロッコリーが新しく指定野菜になります。
Ah, a short and sweet sentence (famous last words)! Let’s see…
“From 2026 on, broccoli will become the new chosen vegetable.”
Sounds a bit weird, but I think I understand the meaning haha, it’s probably kinda like “vegetable of the year” or similar.
日本では人口が少なくなって、市場に出る野菜の量が少なくなっています。
I’d say the first part is something along the lines of “In Japan, the population is lessening and…”, and the second half appears to have a similar meaning, that something lessens. The thing that is lessesing appears to be the amount of vegetables, but I’m not sure what the 出る is doing in the middle of the sentence
Perhaps the second part is supposed to mean something like “the amount of vegetables leaving the markets is becoming less”? I guess I’ll go with that…
So, there the complete sentence:
“In Japan, the population is lessening and the amount of vegetables leaving the markets is becoming less.”
__
しかし、ブロッコリーは最近の10年で30%ぐらい増えました。
“However, broccoli has increased in the past ten years by about 30%.”
I suppose the amount of broccoli that left the shop has increased?
栄養が多いことなどが、よく食べるようになった理由です。
I think here, the first and second part are strongly linked together. Something like
“The reason is that nutrition and many things the like became eating well.”
The meaning would be that the quality of the meals that the Japanese eat became good, I guess? 
ブロッコリーは北海道や愛知県、埼玉県などでたくさん作っています。
“A lot of broccoli, hokkaido and things the like are being produced in the Aichi prefecture, in the Saitama prefecture and so on.”
指定野菜の値段が下がったときは、たくさん作っている農家が仕事を続けることができるように、国がお金を出します。
This is by far the longest sentence, so let’s take a deep and good look at it. The first part, I would translate it as something like “While the price of the chosen vegetable dropped, …”. The next part could be something like “many farmers that are producing continue the work in a way so that they are able to…”, and the last one is probably something like “to get money out of their region”. So, this would be something like this:
“While the price of the chosen vegetable dropped, many farmers that are producing continue the work in a way so that they are able to get money out of their region.”
While it might not be the best English, I think the meaning is pretty obvious 
指定野菜が増えるのは、1974年のばれいしょ(じゃがいも)のあと、久しぶりです。
Last sentence!
Gee, what is that の doing there next to the は?
I have no idea what that is supposed to mean
I guess I won’t make a direct translation for that, but I’ll try to describe what I think is the meaning: “It has been a while since the chosen vegetable has increased, which was when potatoes where the chosen vegetables in 1974.”
Aight, here is the complete text!
Broccoli is an important vegetable in the life of Japanese people
In the country, the Japanese people eat well and the “Vegetable Assignment” decides on an especially important vegetable in life. Now, there are cabbage, daikons, tomatoes, eggplants, spring onions, onions 14 more vegetables.
From 2026 on, broccoli will become the new chosen vegetable. In Japan, the population is lessening and the amount of vegetables leaving the markets is becoming less. However, broccoli has increased in the past ten years by about 30%. The reason is that nutrition and many things the like became eating well.
A lot of broccoli, hokkaido and things the like are being produced in the Aichi prefecture, in the Saitama prefecture and so on. While the price of the chosen vegetable dropped, many farmers that are producing continue the work in a way so that they are able to get money out of their region.
(Again, I’m not quite sure how I should translate the last sentence, so instead, here’s a description of what I think that it means:)
It has been a while since the chosen vegetable has increased, which was when potatoes where the chosen vegetables in 1974.
That was a bit easier than the one from yesterday, but still took me around 30 to 45 minutes 