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I would say go for it! Many outdoor plants do well as houseplants too. Some species may have shorter lifespans if they never go dormant, but many species are able to look nice or even bloom indoors in the winter as well. Here is an example of how Gerbera daisies, usually grown outdoors, are grown and able to bloom indoors, something I'm currently doing:
https://www.gardeningknowhow.com/ornamental/flowers/gerbera-daisy/gerbera-daisies-indoors.htm

Usually, after pollination, the petals will drop as the pods swell for seeds. Unfortunately for humans, this is a sign that the plant is accomplishing the life goal of reproduction. There will be little that you can do to stop this process. This is just a part of nature, and will yield to its reproduction later.

Sorry to hear about your shasta daisy! It will likely recover and bloom later than usual this year. Is it in full sun? Slugs in my yard linger where it is shady and cooler. That's why you hear about slugs and hosta so much. But, if you are sure slugs are your pest, there are effective controls. Here is a run-down of effective options: https://extension.psu.edu/how-to-control-slugs

Some shasta daisies can be short lived perennials. If they did have new growth in spring and were hit by frost they probably were killed. This article may help

http://www.gardeningknowhow.com/ornamental/flowers/shasta-daisy/planting-shasta-daisies.htm

If you determine the type of critter causing the damage it can help with eliminating the damage.

Moles and Voles are often found tunneling around garden beds.
These links will help you.

https://www.gardeningknowhow.com/plant-problems/pests/animals/mole-control.htm
https://www.gardeningknowhow.com/plant-problems/pests/animals/vole-control.htm

It depends on the daisy, and the climate. Some will and some won't come back. In colder zones, there are more that won't come back.