即使 vs 虽然

[Kenny同志]

To me, the differences between 虽然 and 即使 are clear.

虽然 is true, or taken to be true – using “factual” complicates the matter as that would bring up some philosophical issues.

虽然我不会说出去，但这事大家迟早会知道。

(The statement that I won’t let others know about it may be true or not, but the speaker take it to be true)

虽然我很少写信，但是我很想家。

(It is true that I didn’t write to my family often)

即使 is concessionarily hypothetical  

即使我不会说出去，这事大家迟早也会知道。

(The statement that I won’t let others know about it is hypothetical and it is not clear whether the speaker will do so or not. Everyone else will know about it, however, no matter what)

即使我很少写信，我也很想家。（This wording is strange）

As an aside, to me, 即使分手了也要开开心心 means (they) haven’t broken up yet; in other words, it is not true that (they) have broken up. Or you can call 分手了 a hypothesis.

[imron]

For example, how can one explain why many people insist on using 的 in place of 得 and 地 all the time?

That's easy - Sogou pinyin IME and automatic sentence completion

[creamyhorror]

As an aside, to me, 即使分手了也要开开心心 means (they) haven’t broken up yet; in other words, it is not true that (they) have broken up. Or you can call 分手了 a hypothesis.

Thank you for the confirmation, kenny, this is what I thought too. 分手了 is not a definitely established fact - just a hypothesis.

The fact that some people use 即使 as a pure equivalent to 虽然 doesn't mean they're the same - it could just mean those people are using it wrongly (from the standpoint of 'standard' grammar).

即使我很少写信，我也很想家。（This wording is strange）

What if it was in response to someone saying, "你都没写信给爸妈，一定把他们完全给忘了"? Would that be any better? Or still not quite right? (Obviously 虽然 would work perfectly, but I just want to see if a concessionary tone can justify having a fact after 即使.)

How about "即使你说得对，我写信不多，我也很想家哦"?

[Kenny同志]

What if it was in response to someone saying, "你都没写信给爸妈，一定把他们完全给忘了"?Would that be any better? Or still not quite right?

It’s possible but that makes me feel the speaker is protesting that he/she misses his family and again, it’s still a hypothesis. In response to the question, normally I would expect something like 怎么会呢（才不是呢）！虽然我很少写信，但是我还是很想他们.

"即使你说得对，我写信不多，我也很想家哦"?

Like the example sentence I posted, this one is strange too. The answerer is challenging the statement by the first speaker, implying that what he/she said might well be wrong. Using 虽然 can make the sentence way better, or rather you can say 虽然你说得对，我写信不多，但我真的很想家.

Random example sentences/phrases grabbed from the Internet do not necessarily justify a particular usage of a given word. Books are better, but even books are not always infallible.

[Griffyn]

即是，即便，纵使，尽管，all ok

[skylee]

即是，即便，纵使，尽管，all ok

What do you mean by 即是 is ok?