Is it possible to use another merchant apart from Authorize or Paypal?
Depends! LOL. If you are going to use your own Radius server and write your own web based front end for billing, then you can use any merchant solution that is compatible with the api’s you use or write. If you use Usermanager (as we do for our half a dozen or so hotspots), you are limited to PayPal only in the UK.
What is the reason for using a 3rd party radius server?
See above, you would use your own radius server or a 3rd party one if you were not happy with what userManager can do for you.
If you’re starting out, and trying to keep your costs down, go with UserManager. If you need any assistance, I’m local to you and we run a WISP using UserManager. I have therefore been there and done it already.
Can’t speak for “hotspotsystem”. We were actually considering moving from Usermanager to RadManager, however, despite having now paid for a license, we now discover they do not support the typical hotspot scenario of paying for a time period. E.g. if you pay for 1 hour, their solution means a user can connect for 5 minutes every day, for months, until their “one hour” connection time is up. That is not how our business model works. Nor the model of all the other hotspots we have had to pay through the nose to use ourselves when travelling. UserManager uses the traditional model everyone else does, you pay for one hour of time and after initially connecting, the clock starts and does not stop just because you disconnect. So after one hour of time, with UserManager, your time is up and you will have to pay again, if you wish to re-connect after that one hour from initial connection using your new login.
Also with RadManager, if you pay for 1 day, the “day” ends at midnight, every night. So if you pay for one “day” at say, 23:55, you will only get 5 minutes, not one day! So, for now, we will be sticking with Usermanager.
So - when choosing a third party system, make sure you really test out every feature. Except for the really stupid and annoying PayPal problems we have had, UserManager itself has been very good. We would love to drop PayPal, as every time they have raised a payment dispute, they freeze our account and then after two weeks, gives the customer their money back, even if the customer says they don’t want it back as they have received the service paid for! It is a truly crazy system, where PayPal raises a dispute on a transaction, the customer is happy, we are happy, but payPal isn’t. So, be prepared for the basic rule that they are truly a law onto themselves. But it’s also the cheapest merchant rate we can find. We simply can’t afford to pay the ludicrous bank rates of using a portal direct through to our local bank as they still believe that any business run on the internet must be dodgy. 
