1、到处，都，一个挨一个的意思。（kind of like this word "everywhere" in English） 比比皆是：到处都是，形容非常常见（we use this idiom to describe things which happen everywhere or something which is very common） 2、与......相比；和......比较。（kind of like this phrase"compare...with/to" in English. In this way, there's no difference between "比比" and "比起"） 比比过去，我们现在的生活好多了。（you can also say"比起过去，我们现在的生活好多了。"） 3、竞争，竞赛，一较高下。（like this word "compete". And you can also replace "比比" with “比一比”） 他们要比比（比一比）谁游得快。

”比比皆是”好像是成语，“比比”你就当固定词组用吧，这些都是随口而出的词语。

这样的人比比皆是 we don't say 这样的人比皆是 比比 is often used with 皆是，and is really different from 比起 and 竞争. 比比过去，我们现在的生活好多了。 (It's a sentence that you say the same characters twice to emphasize that.It might be asking someone to compare now to the past )看看过去，我们现在的生活好多了。 (In this situation you see.) 比起过去，我们现在的生活好多了。(this sentence might just tell a truth not asking someone to think of it) 他们要比比谁游得快。(We speak the same characters twice.Because it's a habit,whether you use it twice or not you're right)And you can use 竞争,too.But 竞争 might express that you this activity is more competitive.比比 is just comparing maybe just for fun. And one more,他们比(4tone)肩而行，this time you use it to express that they walk shoulder to shoulder,which means they walk together and really close to each other,they form a really neat troop,or there's a big crowd (a lot of people). A more example 比翼双飞,which means two birds fly wing to wing originally ,but it more means couples love each other now. Wow, your questions are so difficult that I thought them for a long time.

1. In the first example:类似的事情比比皆是, 比比皆是 is an idiom, should be viewed and used as a whole. 2. 比比过去，我们现在的生活好多了。 In this sentence, of course you can use 比起， they are exactly the same. 3. 他们要比比谁游得快。 Here, in this sentence, you need pay attention to the word "要", it indicates the future tense. The sentnece can be translated into "They are going to have a competition and find out who swims faster." The implied meaning is the same with 竞争。 But the word 竞争 is much more formal and need an object, more like the phrase "go for", "strive for" "compete for". we dont use it in small swimming competition. You can use it in comepttions like Olympic or bussiness...for example: 他们要竞争的第一。 Tried my best, hope this could help! Good luck!