Which document embedding model for document similarity
You really have to try the different methods on your data, with your specific user tasks, with your time/resources budget to know which makes sense.
You 225K German documents and 45k English documents are each plausibly large enough to use Doc2Vec - as they match or exceed some published results. So you wouldn't necessarily need to add training on something else (like Wikipedia) instead, and whether adding that to your data would help or hurt is another thing you'd need to determine experimentally.
(There might be special challenges in German given compound words using common-enough roots but being individually rare, I'm not sure. FastText-based approaches that use word-fragments might be helpful, but I don't know a Doc2Vec-like algorithm that necessarily uses that same char-ngrams trick. The closest that might be possible is to use Facebook FastText's supervised mode, with a rich set of meaningful known-labels to bootstrap better text vectors - but that's highly speculative and that mode isn't supported in Gensim.)
First, I want to explain my task. I have a dataset of 300k documents with an average of 560 words (no stop word removal yet) 75% in German, 15% in English and the rest in different languages. The goal is to recommend similar documents based on an existing one. At the beginning I want to focus on the German and English documents.  
To achieve this goal I looked into several methods on feature extraction for document similarity, especially the word embedding methods have impressed me because they are context aware in contrast to simple TF-IDF feature extraction and the calculation of cosine similarity. 
I'm overwhelmed by the amount of methods I could use and I haven't found a proper evaluation of those methods yet. I know for sure that the size of my documents are too big for BERT, but there is FastText, Sent2Vec, Doc2Vec and the Universal Sentence Encoder from Google. My favorite method based on my research is Doc2Vec even though there aren't any or old pre-trained models which means I have to do the training on my own.
Now that you know my task and goal, I have the following questions:

Which method should I use for feature extraction based on the rough overview of my data?
My dataset is too small to train Doc2Vec on it. Do I achieve good results if I train the model on English / German Wikipedia?