What is the Best Water Heater and Pump to Use in my Plastic Swamp Cooler (for my Requirements)?

If you're brewing outside, you're going to have to forgo the pumps in below freezing temperature unless you plan on running that pump throughout the brew day, almost non-stop with hot liquid. From personal experience, I've had my march pump freeze up on me in the garage with the ambient temperature around 31ºF sometime between vorlaufing and chilling the wort.

As to heating your mash and maintaining a boil, heat sticks pose just as much of a safety risk as propane. Electricity and water/liquid can be a dangerous thing, so unless you are totally comfortable with working with electrical things (or know someone who is), I'd personally avoid it. You'll want a Ground-Fault Interrupt that you're plugging your unit into, sufficient service to power your heating elements, proper installation of your heat stick, and ensure that things are sealed sufficiently to prevent leaks and potential electrical hazards. But not being an electrician, I recommend that you consult with a licensed electrician before proceeding with that plan.

Personally, I recommend using a space heater of some sorts — like a propane-powered area heater to keep the ambient temperature above freezing. But be sure you have adequate ventilation or you could kill yourself with the Carbon Monoxide. For me, having the garage door up one foot usually works. I heat my mash and my wort with a propane burner, and when I need to rest for my mash, I wrap it up in two layers of the aluminum bubble insulation, held on with a bungee cord. I typically still have to heat and stir my mash every 15 minutes if it's below 30ºF in the garage.

EDIT: not sure I deserved the down-votes. Before the OP was edited, there was nothing to indicate the expressed desire was to control fermentation temperatures, and NOT winter brewing...which is what the content in his question implied.

I do winter ferments in a big plastic tub (called a "muck bucket") full of water. I put the fermenter in that and put a 65W aquarium heater in the water. If it's really cold, the heater runs 24/7. when it's not so cold, I out it on a timer to come on at the coldest parts of the day. With ambient temps in single digits, I can keep steady temps between 50-55F for lagers or 62-65F for ales. Reliable and inexpensive. Also, when the weather is warmer, I can take out the heater and put ice packs in the water for cooling. FWIW, you do not need 1-2F accuracy.