Can doujinshi get anime adaptations? Also can they become "real" Manga if good enough
If by "doujinshi" you mean "self-published manga that parody other published works" (probably the most restrictive definition), the answer is yes. Examples:


Nyoron Churuya-san (a Suzumiya Haruhi no Yuuutsu doujin)


If you loosen the definition to "self-published manga", there are even more examples:


Sore ga Seiyuu!
Getsuyoubi no Tawawa


If you go further and consider all self-published works (including webcomics and text-only media), there are even more:


Maoyuu Maou Yuusha (originally a series of posts on 2ch)
Isekai wa Smartphone to Tomo ni (originally posted on "Shousetsuka ni Narou")
Re:Zero (likewise)
One Punch Man (originally a webcomic)


This is by no means a rare phenomenon. Self-published stuff that becomes popular gets commercialized pretty often.