For the first bullet point, you can do it in gensim 0.11.1
from gensim.models import Doc2Vec
from gensim.models.doc2vec import LabeledSentence
documents = []
documents.append( LabeledSentence(words=[u'some', u'words', u'here'], labels=[u'SENT_1']) )
documents.append( LabeledSentence(words=[u'some', u'people', u'words', u'like'], labels=[u'SENT_2']) )
documents.append( LabeledSentence(words=[u'people', u'like', u'words'], labels=[u'SENT_3']) )
model = Doc2Vec(size=10, window=8, min_count=0, workers=4)
model.build_vocab(documents)
model.train(documents)
print(model[u'SENT_3'])
Here SENT_3 is a known sentence.
For the second bullet point, you can NOT do it in gensim 0.11.1, you have to update it to 0.12.4. This latest version has infer_vector function which can generate a vector for an unseen document.
documents = []
documents.append( LabeledSentence([u'some', u'words', u'here'], [u'SENT_1']) )
documents.append( LabeledSentence([u'some', u'people', u'words', u'like'], [u'SENT_2']) )
documents.append( LabeledSentence([u'people', u'like', u'words'], [u'SENT_3']) )
model = Doc2Vec(size=10, window=8, min_count=0, workers=4)
model.build_vocab(documents)
model.train(documents)
print(model.docvecs[u'SENT_3']) # generate a vector for a known sentence
print(model.infer_vector([u'people', u'like', u'words'])) # generate a vector for an unseen sentence