1. Analog filters are continuous in time and amplitude.
2. Yes, in some digital technologies. Most bipolar and some MOS.
3. Consider registers (FFs) and logic gates as low level building blocks of digital circuits. Although you can further break it down into transistor level, it's irrelevant for the logical function. If you are designing logic ICs, e.g. ASICs you'll know about the implementation details. You also find them in digital logic design text books. Counting a transistor total is nevertheless possible. You can expect up to several millions (even 10 or 100) in recent logic ICs.