I remember some talks some time ago about proofs of nonexistence of Lagrangian Kleinian bottles in ${\mathbb C}^2$ for the standard symplectic structure, mentioning that this were the only compact surface for which the problem were open.
Question 1: Where to find references for the other surfaces?
Question 2: What is the current status for Kleinian bottles? Do there exist written proofs now?



Lagrangian Kleinian bottles
Just googling "Lagrangian klein bottles" returns the following :


* Stefan Nemirovski, *Lagrangian Klein Bottles in $R^{2n}$*
Geometric And Functional Analysis
Volume 19, Number 3 (2009), 902-909, <https://arxiv.org/abs/0712.1760>


abstract : "It is shown that the n-dimensional Klein bottle admits a Lagrangian embedding into R^{2n} if and only if n is odd."


There was a previous result by the same author about the $n=2$ case, but it had a flaw initially, and was completely rewritten. See *Homology class of a Lagrangian Klein bottle*, <https://arxiv.org/abs/math/0106122>


There is also another proof of this result by V. Schevchishin, *Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups*, <https://arxiv.org/abs/0707.2085>


