No space heater needed. Those chicks will be just fine in the garage with MHP. Absolutely no supplemental heat needed aside from that provided by MHP. Those chicks are not even arriving until March.
To set OP mind at ease,
@Blooie held my hand through my first experience with MHP. They were brooded in the house for the first couple of days, just to be sure that they were eating and drinking, and using MHP well. Then, I tossed the littles and their MHP into a box, and trundled them out to their grow out coop. This is MAINE! In APRIL. Temps down to 20's at night, and often down to high 30's and mid 40's during the day. Those chicks thrived and weaned themselves off the heat by the time they were 4 - 5 weeks old.
As for other questions, I'd not shower in the bathroom while the chicks are there. Moisture, plus the extra heat are not a good thing for the littles. I'd not bother letting them out to run around in the bathroom during their in house time. They are infants. While you can take them out to hold them, letting them run around on the floor will be more of a pleasure for you, than it will be for them. Food, water, heat, shelter are the things that will please them.
If you want to save yourself the work of building that brooder (Are you really going to be brooding chicks often enough to justify the expense?) you might consider other options. IF you are not going to be brooding chicks every year, perhaps you'd rather build a tractor, that could double as a brooder, yet get used in the yard for your birds past their chick days. If you are a gardener, build a tractor that would fit over a garden bed that would match it in size. Or simply save your money, and use an appliance box. You can just keep topping off the shavings in your brooder/tractor/appliance box until it's time to move the chicks to the coop. Then, if you've used an appliance box, you can simply break it down, and use it and the shavings to line your garden paths.
I can't speak highly enough about the benefit of MHP for brooding chicks. After using this system, I'll never go back to a heat lamp again.