Short answer: yes
This is a very broad question, so I won't go into excessive detail about every aspect. I think you should also take a look at BreezeJS because it makes things building these applications significantly easier.
DESIGN
Do you want to build in pure HTML and JavaScript or incorporate CSHTML? The decision is yours, but if you want to eventually create native-based applications using something such as PhoneGap Build, you'll want to stick to pure HTML and JavaScript so that you can compile the code later.
Do you want to use another JS library such as BreezeJS to make life a little easier when designing your controllers? Out of the box, your Web API controllers will be prefixed with api/{controller}/{id} in WebApiConfig. You may want to add {action} routing if you don't go with something like BreezeJS so that you can have more flexibility with your controllers.
Lastly, let's talk about the Repository Pattern and Unit of Work Pattern. This is a bit of hot-topic, but I find that usually creating a repository allows you a great deal of flexibility and it's great for dependency injection. Adding an additional repository layer to your controllers allows you to differentiate between different users or means of access such as a SPA or mobile application very easily. You can use the exact same controllers, but simply draw from different repositories.
SECURITY
You'll want to touch up a bit on [Authorize], [ValidateHttpAntiForgeryTokenAttribute], [Roles("")], and several other data annotations for starters. This is a huge topic which has a ton of reading material online -- invest in some research. Your controller can have multiple actions which have varying limitations on them, such as preventing CSRF on the SPA, but be less restricted on Mobile by either utilizing varying actions on the controller or drawing from separate repositories.
Can I add multiple routes that map to the same method?
https://myapp.example.org/api/todo
https://myapp.example.org/mutual-auth/api/todo
Yes, absolutely. You'll just have to do some extra work with your routing configuration files. With BreezeJS, you get access to not only /api/ but /~breeze/ which works very similarly.