It is a question of grammar. You're looking for a word to qualify the way A and B are used, in the construct “to verb A and B qualifier”. This qualifier has to be an adverb (“a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word-group”).
Now, you want to express parallelism. “Parallel” itself is an adjective, as well as a noun and a verb. It is not an adverb, and as such, cannot be used in “using A and B parallel”. The natural adverb that derives from parallel is parallelly; though it's not exactly very common in general usage, it does exist and is attested in multiple (though not all) dictionaries. So, “using A and B parallelly” works.
Regarding in parallel, it so happens that it is a common phrase meaning “occurring at the same time and having some connection”. It may be more commonly used than parallelly, which is why it would feel very natural in your sentence, but both are correct.
"According to so-and-so" is a well-accepted phrase to indicate a certain level of authority. It doesn't mean authority in the sense of indisputable, world-class, absolute authority. It means authority only at the level of indicating that this is the person to whom the statement can be attributed.
It therefore has rather wide usage, all the way from according to my brother, Nancy went to the dance with Frank, right on up to according to Einstein, the universe is curved.
The lowest level of its reference to authority, however, is the second person, according to you, which sometimes is used sarcastically, thus: According to you, I should never have bought stock in Microsoft. Boy, were you wrong.
We don't take it down to the first person, because that becomes overly emphatic, or to put it another way, redundant. According to me is simply saying, this is what I say. It isn't considered necessary to say this is what I say when you say something. You just say it, don't you? I can tell you Nancy went to the dance with Frank without saying According to me, Nancy went to the dance with Frank, you see?
If we look at your examples, Mari-Lou, we can see a little bit more of why the usage sounds a bit strange to native English speakers. Since we do imbue a bit of authority to the according to locution, we usually feel according to my brother, our father will go to a nursing home someday does sound odd; we would instead tend to say my brother thinks our father will go someday, and the response would be but I don't think so rather than according to me he won't. According to in standard English usage is given some weight of authority, even at the lowest level. It isn't taken as purely opinion.
Best Answer
Mom and my mom are very different: it is not simply a question of possessives.
If you and your siblings shared, say, a truck, then you would simply use the appropriate pronoun:
Of course, you could apply the construction to mom:
This is still a bit unusual, primarily because Mom is often used as a proper name. For example, you might say:
However, the name Mom is usually used within one's immediate family. I might say "Have you talked to Mom today?" to my brother or even father. This is despite my father, clearly, having a different mother than myself. But I would not use the name Mom when talking to someone outside my immediate family; instead, I would say my mother.
Of course, this last point is not a matter of grammar. The question of who is allowed to use a term of endearment has no definitive answer; it depends on personal preference and cultural norms. Even within the English-speaking world, different people may have different standards for who uses the nickname Mom. To the best of my knowledge, my analysis is fairly standard for white Americans in the Mid-Atlantic. But other groups may have different usages.