It is often simple to start from the basics, so :
私のペンです。
My pen
So the pen is the item owned. We can then substitute pen for 好きになる人 (person to fall in love with) for :
私の[好きになる人]
My (person to fall in love with), so the 私 is the one who falls in love with the 人.
それに私の好きになる人ってクズみたいな男ばっかだからなぁ
Moreover, the person I fell in love with is only interested in trash things.
Not sure how to separate the sentence so I tried it in one go.
Plus, I think I read the beginning of that manga so free context for me 
Little late on this one - but I feel like my manga shelf obligates me to translate this.
フリーザはサイヤ人の底知れぬ可能性をおそれている
Frieza is afraid of the unlimited power potential of the saiyans.
EDIT - Mistakenly translated 可能性 as power instead of potential.
それに私の好きになる人ってクズみたいな男ばっかだからなぁ
In addition, it’s because people I like are only men who are losers.
This one was more difficult to parse than usual, but this is what I came up with:
私の好きになる人 - “people I have come to like”って - casual form of は, the topic particleクズみたいな男 - “loser-like men”ばっか - short form of ばかり, means “only” or “nothing more than”だから - “it’s because”なぁ - ending particle usually expressing talking to oneselfそれに私の好きになる人ってくずみたいな男ばっかだからなぁ
Moreover it’s because the persons I fell in love with are only men looking like dullards!
自分の翻訳のなかでたくさんのことに自信がありません。「ばっか」とは「ばかり」の略語だと思っているけど自信がありません。それに「って」は「は」の助詞と同じだと仮定しました。
Besides, it’s because the men (s.o) falls for are merely losers.
気持ちが良くなるように風呂に入ったほうがいいよ。それに君の髪が臭いんだ。
Dogs can’t sleep in the wild.
I don’t have alot faith in my translation. I thought “ばっか” was an abbreviation’ばかり’, but I’m not confident. Moreover, I assumed the ‘って’ particle as the same as ‘は’.
Besides, the only guys that I end up liking turn out to be jerks
それに - kind of hard to translate this taken out of context. Could be : also, in addition, plus, besides, etc…
私の好きになる人って - lit. The people my liking becomes
くずみたいな男 - lit. Guys that are like trash. I decided to go for a family-friendly translation here with “jerks”, but some more explicit language would work just as well if not better. 
ばっか - slang for ばっかり/ばかり
だから - because
なぁ - sentence ending expression that reflects things like yearning, regret, envy, etc…
September 18th Translation
Notes :
For common words like ばかり that are used for emphasis, there are often lots of different variations that can be used. Usually if you read a word that looks somewhat like a word that you are used to seeing in that position in a sentence, there is a good chance that it is just a slang variation of the one you know.
This is alcohol/alcoholic.
In accordance with the law, age verification is being implemented.
Liquor will not be sold to minors.
Hey, you added the text! 
Due to the law, age verification will be enforced. Alcoholic drinks will not be sold to minors.
My first thought when I saw ばっか was “jeez, they’re already losers, now they’re stupid too?” Then I realized it was a variation of ばかり and not バカ. 
Like you suggest, バカ wouldn’t really fit in that place in the sentence though so that was my first clue.
Yep! we will add it to everything from now on 
It only takes a few seconds extra and if it encourages more people to have a shot at it, then it is time well spent! 
This may just be a convention that I have noticed in all of my reading, but another small (but potentially helpful) thing to keep in mind is that adverbs/particles and similar words will usually be emphasized through use of the skip-mora（っ） ばっか, whereas nouns are far more likely to get emphasized through elongation（ー） バーカ.
I would say that this is a pretty regular occurance, and may just be a speech/language habit, rather than any sort of grammatical rule.
I hadn’t thought about that before, but that is really useful! Thank you for the tip! 🙇♂️
法律により、年齢確認実施中です。未成年者には酒類を販売しません。
法律 = Law; Statute
により = According to; by (means of); due to; because of
年齢確認 = Age verification
実施中 = Being carried out; Being put into practice; In operation
です = be; Is
未成年者 = Minor; Person under age; Minor (law)
には = As for; regarding
酒類 = Alcoholic drinks; Liquor
を = Indicates direct object of action
販売 = Sales; Selling; Marketting
しません = Negative of する (to do; to carry out; to perform)
Rough : Because of the Law age verification is being carried out. As for Persons under age, Alcoholic drinks will not be sold.
Natural : Due to the law, age verification is carried out. Minors won’t be sold alcohol.
A lot of vocabulary I hadn’t come across before ^^
“Due to the law, age verification is being carried out. Alcohol will not be sold to minors.”
By law age verification will be conducted. Alcoholic beverages will not be sold to minors.
According to the law, we verify the age of customers. We do not sell alcoholic drinks to minors.
