"There is a table in front of me."
No, it doesn't match the focus of the English sentence. In your version, the table is the topic and feels more like "THE table is in front...", like you're talking about a specific table. Also, if you feel like this sentence really needs a topic you could write 私の前には... Making the location also the topic. Dou accepts this, but I think it feels like the focus is too much on the location instead.
That's not right. は is the topic-marking particle. In plineder's sentence, テーブル is marked by は, so テーブル is the topic.
What is missing is the subject. が is the subject-marking particle, so the subject, if present, would be marked by が. However, in plineder's sentence, the subject has been omitted, so the が particle is omitted, as well.
Omission of the subject is allowed by the grammar of the Japanese language. The subject will often be omitted if it can be deduced from the context.
Hmmm, ok, yes, you can move the 前に around without changing the meaning. It'd be like if you started the sentences and suddenly realized you wanted to point out that it was in front of you. So in English your sentence reads like someone adding a thought to a sentence, "the table is, oh, in front of me I mean." It's not wrong it's just not proper or very fluid. The reason it starts with まえに is because then with context clues the speaker might be able to not say the rest of the sentence. If we were talking about where my car keys are in relation to the table you might simply say "in front of". Japanese prefer inferred meaning to spelling things out. So if you can answer simply with "in front of" that's ideal. Hence, 前に, direction, is first.
Is there a difference between the 一 (いち) and ー (symbol next to れ on my jp keyboard) ?
Some rather random experiments seem to suggest there is, but it seems weird to me as they appear identical. How would the second symbol be pronounced in isolation?
I understand that in テーブル it is used to enlongate the て sound.
The ー that is in テーブル does not have a pronunciation on its own. It is used to extend the sound of the kana before it. So in this case it extends the sound of テ by one unit of time (or mora). ー is used with katakana. The list [あいうえお] has the similar effect of extending the sound of previous hiragana.
As far as I know, as long as the verb is at the end of the sentence and if there's a topic - the topic is at the start (there's only one exception - I read that sometimes time can go before the topic), then the sentence would be gramatically correct. So you can switch the places of 前に and テーブルが. Maybe it would sound more or less natural but I don't know about that yet. You can check out https://d81pp4ybbpmjf.cloudfront.net/80-20-Japanese_Sentence-Structure-Cheat-Sheet_A4-hiragana.pdf for more info on sentence structure.
We say [something]は...が... when we say something has a property/trait.
e.g. 私（わたし）は背（せ）が高（たか）い I am tall. 背が高い is tall. So I have a property of tall.
e.g. 東京（とうきょう）は人（ひと）がたくさんいます Tokyo has a lot of people. Tokyo has a property of a lot of people. We can say 東京には人がたくさんいます (which is better)
Now 私の前 is not a thing or concept that we take to describe a property. It is a location. So it is not natural to say 私の前はテーブルがあります. It has to have the existance particle に. It can be either 私の前にテーブルがあります or 私の前にはテーブルがあります. は is bringing the phrase 私の前に to a topic.
From what I gathered (from 語源由来辞典 http://gogen-allguide.com/), it seems before Edo period, these pronouns 貴様、お前 had the original meaning (honored you). In Edo period, people started using commonly among the public, and the level of politeness decreased. They even became rude in late Edo period.
This exercise confuses me because I don't see it saying "me." To me it just looks like the table is in front.
Well, personal pronouns are usually omitted because they're already implied. But, frankly, I find this particular expression pretty weird. I don't think even Japanese would say it specifically like this, unless they're describing the location of the table in some context (which is not provided here).
How do I say it is in front of him?
Technically it is possible to say 僕の前はテーブルがあります like 東京は人がたくさんいます in the other exercise, but it is very rarely that 僕の前 moves up the topic and even with に dropped (僕の前 is rarely significant enough to become a place of interest).
So for the sake of beginners, please stick to [location]に[subject]が/は あります/います.