1. Which indoor plants stay alive in a hanging basket and look fresh all year round? I don't want them to be seasonal only.
All of the "typical house plants" but in different locations, depending on which way the windows face.

2. Will ants and other insects get attracted to multiple basket plants around the house
Not unless they are in the house anyway. Insects that specifically attack plants are unlikely to show up if the plants are healthy.

and is there an easy way to prevent them?
Make sure the plants don't have ants when you bring them inside.

3. And can you recommend any particular all-year basket plants that fragrance rooms? Or some that will smell good during season 1 and 2, and then other plants that will smell good for the other seasons?
What way do your windows face? Are you going to buy new plants every 6 months? If not, where will the "off season" plants go? Are you looking for fragrant flowers, or would you also be interested in foliage that has fragrance?

Flowering indoor plants are generally fussy prima-donnas and from experience I say growing any plant for the sole purpose of fragrancing (spell check says that's not a word, too bad, I'm saying it) the great indoors usually ends in frustration and disappointment, no odor if you're lucky, a bad odor if not. Well, just kidding about the bad odor, but the leaves just don't offer any excitement in that area. If you don't like a Jasmine or Gardenia plant without flowers, it's not for you. The other heartbreaking truth is that most of the really "wow" smelling flowers are sporadic. The constant bloomers tend to be totally ungifted (sorry spell check, channeling Archie Bunker, shhh!) by fragrance. So I would ask, can you love leaves?

Now, I want to see what others say because there's GOT to be something I just don't know. I want this plant too!

"which indoor plants stay alive in a hanging basket and look fresh all year round? I don't want them to be seasonal only."

Sorry, don't mean to sound mean, but as far as I know plastic or silk will be the only things fitting requirements of your number 1.

Thanks purpleinopp. Some areas of the house are darker with less natural light. I'm really looking for plants to hang neatly around the home on bare-looking walls.

I also thought I'd be out of luck with year-round frangrant plants. You make a good point about what would I do with semi-season plants. I really don't want to have to maintain them so much.

I don't mind fragrant green foliage plants if they give a general year-round fragrance (if that is what you mean?). Which ones would these be?

If I can't find fragrant ones then I guess any low maintenance plant that can live in a basket all-year and still look good will do just as well. It needs to be fairly hardy and tolerate various lighting. Really don't want to go the plastic route :(

Well, I'd assumed you'd want to hang the baskets right in front of the windows but it sounds like that's not the case. The aromatics I can think of would need lots of light, and I just noticed you're in UK, so that may not be possible indoors... Rosemary, creeping Thyme, scented Geranium, Plectranthus, Basil.

You might get a lot more satisfaction from having a collection of different plants than many copies of the same one. Are there stores near you where you can browse the plants to see which ones are attractive to you?

The old stand-bys have honestly earned their reputations for being undemanding and tolerant of varied conditions, as long as you don't overwater them, pothos, spider plant, heart-leaf Philodendron, Tradescantia zebrina. Pics of these are easy to find (as are the actual plants):

Here is a link that might be useful: Google image search