The purchase is a one time cost and provides for an unlimited use on any number of computers for the current version and the next major release, upgrades past this are at a 50% discount. Moneydance syncs between all instance on all supported Operating systems. The Mobile apps (Android and IOS) are helper applications designed for mobile data capture.
There is no time limit on the trial, I do not know where this idea is coming from. The trial limit is 100 manually entered transactions with an unlimited number of imported transactions. In trial mode all functionality is active.
I can only offer limited comments on budgeting since I do not use it. Budgeting is designed around spending money not in the source it is coming from.