Even if economic or feasible it still does not change the fact that without heat,life cannot exist.Heat comes from the Sun or the transition of matter from one form to another.On Mars the sun cannot provide adequate heat because of the distance so energy must be expended to create it.
This idea that Mars once had life is just another way that huminists attempt to push creation off the table.
That would just about do it, though, wouldn't it.
Not at all! You're still thinking "in the box". You can divert a comet's path with a relatively miniscule amount of thrust, as long as you do it far enough away. A change of a fraction of a degree out in the Oort cloud would completely alter the path of a comet, and be relatively simple to do in terms of energy expenditure (you could do it with a conventional chemical engine, or even using the comet's own volatiles as reaction mass, if you wanted to get fancy). Calculating the exact change needed is the tricky part, and it's not THAT tricky.
In terms of melting the Martian polar ice caps, that's even simpler. Seed them with a genetically engineered plant that can thrive in the cold sparse atmosphere, but which (here's the key) is dark. You don't need to make that many, because they'll spread on their own (think ivy or kudzu). You lower the albedo of the poles, they retain more of the energy they receive from the sun, and they begin to melt. Soon, the amount of CO2 in the atmosphere is large enough to get a greenhouse effect going, and the process accellerates.
I'm not saying it would be a cake-walk, or quick, but it's certainly not a prospect that can legitimately be dismissed out of hand. Check out The Mars Society for a group of folks who have thought this stuff out a lot more than I have.