Why is there 后 in...
What is the function of 后 in 他会大概二十分钟后到 as "She will arrive in about 20 minutes,"?
Why is there 在 in 我总是在星期六去游泳? Shouldn't it be omitted? Also, why isn't it 我在星期六总是去游泳 instead?
Is 他吃完饭会马上刷牙 equivalent with 他吃完饭以后会马上刷牙?
Is 我的刷牙习惯是每天三次 the same with 我习惯每天三次刷牙?
后 here means "after". The sentence says that after about twenty minutes have passed, he will arrive. The word "in" plays a similar role in the English translation that you gave.
在 here indicates location (in time). I think the second Chinese sentence makes less sense because it looks like it is referring to a single Saturday, rather than to every Saturday.
I think you don't need 以后 here because 会马上 indicates that the one action will happen immediately after the other.
To build on what @floer said..
后 here is just short for 以后. Chinese is a relentless language when it comes to mitigating grammar. So often times two character prepositions or postpositions are reduced to single characters, and many times, they can be left out altogether if it is already clear. (This partners strangely with Chinese penchant for redundancy in content words.)
In this case, 在 is being used like the English preposition "on" so 我在星期天去大连 would be "I am going to Dalian on Sunday." However, note that 在 also has other uses for time. Just like 后, 在 is short for 正在, which means "while" or "during." For example 我正在考试 would mean "I'm in the middle of taking a test." As a side note, the equivalent for "before" is 前 which is short for 以前.
So for example:
吃饭后 = After eating. 在吃饭 = While eating. 吃饭前 = Before eating.
Three. Those sentences can be generally understood to communicate the same information, though you're obviously aware that one of them has added an extra qualifier specifying 以后. However, I've never heard people say both 完 and 以后 together like that. This is because both 完 and 以后 both serve the function of marking the completion of the action, so we understand what triggers the 马上 segement of the sentence. There's a few ways you could do this and you only need to choose one:
3.1. 完 -- 吃完饭马上会刷牙
3.2. 后 -- 吃饭后马上要刷牙
3.3. 了 -- 饭吃好了马上要刷牙
Four. Both those sentences are intelligible, but I think that the first one might seem a little wordy in Chinese, and it makes a classic English mistake of ignoring a perfectly good verb in order to use "是“ as the to be verb. This comes from the English language habit of favoring the to be verb, but that's not the habit of Chinese folks, and they will kinda chuckle at you for doing it. (I know because I'm guilty as well.)
In this case, you're using 习惯 as a noun, meaning "habit" but in Chinese, the line dividing nouns from verbs is fluid, so 习惯 can also be a verb meaning "to be accustomed to." The result is that you don't need another verb to make the sentence work, and can just directly say "I 习惯 brush my teeth three times a day."
There's a deep Chinese aesthetic in understanding how to use words creatively as nouns and verbs, and getting a feel for it really opens up the language for you.
The two sentence mean more or less the same thing but have completely different underlying messages:
[我的刷牙习惯] [是] [每天三次] [My habit of brushing teeth] [is] [three times a day]. (Talking about brushing teeth, I have a habit/routine and it's three times a day.)
"我习惯每天三次刷牙" [我] [习惯] [每天三次刷牙] [I] [am used to] [brushing my teeth three times everyday]. (I am used to brushing teeth 3 times a day, not just once or twice, this is what I have got used to and feel comfortable with.)
The more 'native' way to say the second sentence is: 我习惯每天刷牙三次. or 我习惯每天刷三次牙.