My answer would be maybe to both questions, but aphids are actually pretty easy to get off of indoor plants, usually: a good spraying of the foliage with a kitchen sink sprayer or a detachable showerhead, and they fall right off and go down the drain. You might end up having to repeat the spraying, but the one time I've had aphids on an indoor plant, all I needed was the kitchen sink and five minutes.

I guess the first mistake was in bringing in the plant when it was so infested.
Outdoor plants and those that normally spend time indoors but go outside in good weather, should be inspected before bringing indoors so that easy spraying outside can be done without the danger of sprays where they shouldn't go...like on furniture or on pets.

The plant, if it can be taken to a room that you can spray water effectively, is the place for it. Perhaps the laundry room tub can be utilized to spray the plant top to bottom and covering all surfaces, will usually do a good riddance of aphids.
Also, if you can see the bug, then picking off and squeezing between thumb and forefinger is an accepted method to be rid of them.
Generally some insecticides do more harm than the pest so you should identify the pest before spraying and let the insecticide be for the pest.

Soap is a good treatment. It smothers bugs and does no harm to the plant if rinsed off after 10 - 15 minutes.

Pyrethrum and rotenone are also recommended to treat aphids....but do the water first.

Rotenone really shouldn't be recommended for indoor use. It's actually quite toxic.

I suspect that your ivy would be fine outside on the porch. Very cold temperatures would kill the adult aphids but they've already laid a crop of eggs in the nooks and crannies. The eggs WILL overwinter and you'll end up with a big population of aphids in the spring that seemed to appear out of nowhere!

Soap sprays won't do much to kill the eggs, I don't believe. Frankly, I'd cut the plant all the way back to the soil (or nearly so), so that you can start fresh and aphidless.

Next season, keep a watchful eye out and be prepared to spray with plain water, commercial insecticidal soap (don't rinse), and/or a horticultural oil of some kind.