I don't think there is a differentiated cell (or any cell) that transcribes all genes. In every type of differentiated cell, there are only a few sets of genes that gets transcribed and all with different levels. For example, if a stem cell differentiates into a heart cell, troponin genes are transcribed more but proliferation genes are shutdown. A number of terminally-differentiated cells suppress expression of certain genes especially proliferation genes, pro-death genes, and undifferentiation genes to name a few. There are thousands of publications regarding transcriptome changes during differentiation and we can see that not all genes are expressed at any given stage.
1. No, some genes are tissue-specific (they only get turned on in specific tissues), some genes transcribe only during specific development stage of the organism.
It will not express embryonal, or tissue-specific genes (Except of course those from the specific differentiation state these cells are in). And of course some genes are only expressed upon stimuli (radiation, virus infection, IFN, LPS) if you are looking for a broad source of expressed genes, I would probably recommend whole mouse embryos or newborn mice (and even there......(see above)). However at VERY low levels you might find almost every gene in almost every tissue (And I mean V E R Y low)