You have asked quite a few questions in this post.
When should I use grouped(toggle) buttons in place of radio buttons?
I think the toggle buttons are the more contemporary implementation of either/or selection. Radio button being the former. If you are going for a modern look, you should think of using toggle buttons. Reasons include,
- More hit area for selection for an option in case of the toggle button. Radios don't always work on labels.
- Possibly easier to grasp the selected option because there is no cognitive load for associating the right label with the right radio.
Couple of problems
- It is important to note that toggle buttons don't work well with options having longer text length. Top to bottom radios work well in such cases.
- It is hard or unconventional to show tab-based keyboard navigation on toggle buttons. Users are well-versed with tabbing on radios than toggles.
Then why not use a drop-down?
The biggest problem of dropdowns is that they hide values. Users need to go and open the drop down to see possibilities. Radios and Toggles show data upfront. If real estate allows and the number of options is very small, one should go for radio buttons/toggle switches.
Dropdowns on the other hand, handle scalability very well.
Should I do away with the radio altogether if I use grouped buttons?
I would be wary of mixing the two metaphors. I would stick with one. As a user it might confuse me on what basis you have chosen a radio vs a toggle.