There are two answers for it. It depends on what accent you use. If you say "你写的很好".It comments on the words you wrote. If you say" 你写得很好," It comments your meaning and expression are great.(not really foucus on the single words). So both of the sentences express different meanings. Actually, the native speaker knows 的 and 得 well.

This is a complicated question. Grammatically, you are right (写得很好). We used to distinguish those three "de" (的、地和得). But as I know, nowadays, students in China are not asked to do so any more. I guess that's why you saw some chinese wrote this in a "wrong" way. But in my opinion, it is better that we still use them grammatically correct.

I think basically what needs to be said has been said. But as hw3k6i said, 你写的很好 still makes sense and therefore is actually not grammatically wrong. The original version of the "N1 + V + 的" pattern is "N1 + V + 的 + N2", which is a relative clause that can be seen as "The N2 that + N1 + V" in English. When N2 can be inferred, it's very often dropped and becomes "N1 + V + 的" only, which can be seen as "what N1 + V" in English. Therefore, 你写的很好 can be seen as an easy way to say 你写的 (文章/东西) 很好. I think you have known the "N + V + 得 + adv" structure well so I won't go on and rant about it. Here's a practice. What should it be when you hear "你做 de 很好"? Is the pinyin part for 的 or 得? The answer is: it depends. 你做得很好 means "You did/does well". 你做的很好 means "What you did/do is great".

这没什么好稀奇的，用拼音打字的人经常懒得去选正确的字。

That is common. But native speakers don't really get mixed up between"的"&“得". We all can use the correct one when we are writing.But when we are typing,it is so troublesome to choose the right one from the options,so most of us will use the one comes up first.It's more convenient and saves time,especially when we are chatting online with others.