1. Yes, you can use LED bulb replacements and incandescent bulbs in parallel on the same circuit, without a special flasher. You can flash them on and off with the incandescents. The only problem you might run into is replacing most or all of the incandescents with LEDs which may not draw enough current to heat up the element in the flasher. In that case, you use an equalizer in parallel with the LED lights. It's just a resistor that increases the current draw through the flasher.
2. No, you cannot use most LED bulb replacements with a standard dimmer, at least the way the dimmer is intended to be used. Quality LED lamps have a current regulating integrated circuit feeding typically three white LEDs in series. If the voltage feeding them reduces current too much the IC quits functioning and they quit conducting. Cheap LED lamps have just a dropping resistor in series with one or more LEDs. The more LEDs in series (meaning the smaller the dropping resistor), the quicker they dim with a voltage drop. They dim much quicker than incandescents with a lot less voltage drop, in other words from bright to off in only part of the dimmer's range. You can build your own dimmable LED fixture with a variable resistor controlling the the IC.
3. Yes, you can save power with a dimmer, however with cheap ones that just increase resistance, the light level goes down faster than the current and power is wasted as heat across the resistance. Good DC dimmers will use electronics to maintain full voltage but turn the bulb on and off faster than the eye can see to reduce the average power.