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Well, as for me гастроном is a kind of word nobody uses anymore. We usually refer to any kind of shop as just магазин and if you really want to refer to a grocery store you say продуктовый магазин

Я предлагаю пойти сегодня в Третьяковскую Галерею. - Correct. Not sure about you present tense theory though. :)

Так как Лена знала, что у Маши нет машины, она попросила Павловых заехать за ней....

That's imperfective because it's the same "stretched in time" thing I explained you before. It's like TILL a certain moment no one had ever invited him.

However, let's contrast this thing.

Но...

Майя вышла замуж за Андрея Шаховского
Аня наверное предложит поехать на дачу не сегодня, а завтра

будет предлагать assumes that this action would be stretched in time, but we see a perfect...