Yes, tokens will be mined, for the latest plans see https://forum.blockstack.org/t/improved-mining-algorithm-min...
We conducted an economic audit and as a result of that study made certain changes to future supply of tokens. Details are in the forum post linked above.
The token economics 2.0 paper is not published yet but the bulk of the details are in that post. We outline the open challenges in the "adaptive mint/burn" mechanism for future token supply there as well. Basically researching optimal values for the "evaluation window" and if we should have a maximum cap on mints i.e., tokens that re-enter supply after being burned/used.
Initially, we rely heavily on proof-of-burn when the native hashpower on the network is lower. We're currently looking at memory-hard hash functions for the native PoW part.
You may want to look at asymmetric memory-hard PoW as well (instant memoryless verification)