"My older brother is next to the table."
"Tonari" means "close to" not specifying if it is in front, in the back, to the side. Just close to it. "Yoko" means more "to the side" of it. You would not say "yoko" if it was in front or in the back. You can also say "ichiban tonari" as the "closest" object of many, even if it is really not that close.
Copied so people don't need to click it
"Tonari (next to; next door, neighboring) and yoko (side, next to) are used a little differently than their English counterparts.
Things that are tonari must be of the same type, caliber, or quality. They must be perceived in some regard as equal. You cannot say: kare wa tsukue no tonari ni imasu (He is next to the desk.)
Tonari is also used to refer to the nearest object of the same type, regardless of whether the actual distance is near or far. Also, a neighboring house, or a person living in a neighboring house, is called tonari, or the more polite otonari。
Things that are yoko are right next to each other. With yoko, size and quality do not matter."
How do you know what to start the sentence topic with? I feel like I'm just guessing half the time.
Sometimes I would start with older brother...etc and other times with say, table for example. The syntax is so confusing. It doesn't help that sometimes duolingo just swaps it adound at what appears to be complete random. I feel like every time I adjust, it's the wrong way.
How is it that you can tell with what the topic is supposed to be??
It doesn't help that sometimes duolingo just swaps it adound at what appears to be complete random
this is a huge can of worms that I'm not sure you wanna open right now, but here is a good article that does a good job at explaining the basis on how japanese people think when organizing information in sentences.
How is it that you can tell with what the topic is supposed to be??
the topic is whatever you need to talk about it, and it's always marked with は or omitted because is obvious by context. You wanna mention the position of something? that can a be a topic, you wanna say something about the dog? that's the topic, you wanna describe a person? that's the topic. In this case the topic is your brother because you are saying something about him.
The answer you proposed is now accepted.
I think which version you pick corresponds to whether you think of this English sentence as answering the question, "Where is your older brother?" or "What/who is next to the table?" (or even perhaps as a somewhat broader reply to "Is there anybody/anything next to the table?").
Duolingo's sentence takes the older brother as given, so it corresponds to the first question. Your sentence takes "next to the table" as given, so corresponds to the second.
The structure in your example would be translated as 'There is my older brother next to the table' or 'Next to the table there is my brother'. Subject/Object inversion makes this sentence somewhat unnatural.
If you wanted to say 'There is an ant on the cake' you would say ケーキの上にありがいます。But, if you said ありがケーキの上にいます it would mean 'The ant is on the cake'.
The point of this sentence is to answer the question 'Where is your big brother?'.
As a reply to said hypothetical question, 'My big brother' should be the topic and following the more standard AはB sequence. Placing 'big brother' at the end diminishes its relevance as the topic. Try to keep the topic at the head of the sentence for now.
テーブルのよこにあにはいます。 While it makes sense and means the same thing, it doesn't sound natural. That's the main issue.
let me try
Honorifics are there to be respectful with other people, if you add ご to 両親 that probably mean you are talking about the other people parents right? because you are trying to be respectful of their parents in from of them.
兄はテーブルのよこにいます implies you are part of the group of this "older brother" because you are skipping both honorifics, it's probably your older brother because it doesn't make sense in other ways.
so why would you ever use 兄さん? well if you wanna be respectful with your brother but not you don't wanna be so cold in from of him, if you skip the お in this case implies that is your own brother but at the same time you wanna be respectful so you add the さん, this is very slangy as BJCUAl said because you usually say other's people names when speaking to them or just skip it because it's obvious.
兄さんはテーブルのよこにいます sounds weird because it's obvious you are talking about your own brother (you are not using お) and you are talking about it with another person. It's like you are implying that your brother is superior than them and this is seen as rude. So you use 兄は when speaking about your brother with another person in order to be respectful with that person you are speaking with.
で is for location where an action is performed. に is simple location (existence).
The に particle has different functions, one of which is to indicate movement towards something, but that would be attached to いきます (a motion verb), not います (a verb of location or existence).
で also has different functions, as do most particles.
Imasu is for people & animals. Arimasu is used for inanimate objects.
There is some change when you are talking about smaller organisms, anthropomorphised objects, or speaking about the deceased body of a human or animal. For the vast majority of cases, however, remembering this distinction is very important.
'Oniisan' is generally used when referring to another person's older brother, while 'ani' is generally used to refer to one's own older brother (direct address of one's own older brother, however, will normally use 'oniisan' or 'aniue' 兄上).
テーブルは兄の横にあります means "the table is to brother's side""
兄はテーブルの横にいます means "brother is to the table's side"
Just think on what you are trying to say, in this case you are trying to speak about your brother, that's the topic, hence you mark it with は as in 兄は, while the table's side can be translated it to テーブルの横に, then you add the verb "it exits" or います
You also use あります if you are speaking of inanimate objects, while you use います for animated things like human beings
the use of 隣 vs よこ is explained really well in the comments above, as for the use お兄さん vs 兄 I don't see a problem in using honorifics with your brother, but you usually skip it when talking about your family with other people, this is done in order to be humble about your group.
います and あります are basically the same, just with います being used for people/animals and あります being used for plants and inanimate objects in general. You should consider these two to be within the same category: existence ('There is/are').
When a noun is followed by に and then either います or あります it denotes location of existence (is at/is in).
My older brother is located next to the table (at the table's side).
The scratch is located on the right side of the table.
です is normally only used in sentences such as 'A is B', showing correlation (I am/he is/they are).
That is the table leg.
Now, in colloquial Japanese, some people might occasionally substitute です for にあります. This is non-standard and DL would be unlikely to propose or condone such usage.
テーブルのよこです could be seen as a colloquial shorthand for テーブルのよこにいます.
The difference between です and います・あります is oft-inquired of. Here's one such thread. I suggest you peruse a few explanations until it is clear to you.