Slow syncing (large chain) -- being worked on. Syncing blocks after disaster is actually 100x faster. Once pruning is implemented we can put up some "agreed upon" pruned chain (maybe domob can add some sort of rpc which prunes/normalises so everyone has identical output (pruned chain) so can make sure is legit (produces some hash?).
So the slow syncing is caused by those many hunters on the chain/map or by some bugs, right? Will it be worked out in theory? Will the pruning be repeated from time to time? Apart from the first pruning, will the following pruning have no effect on the game state? Thanks.
If you wish to call it a "bug", yes. The amount of transactions processed by Huntercoin is just order of magnitudes larger than any other altcoin I know of (the pure chain is almost half that of Bitcoin, with a much shorter life-time so far) - thus it hit the limits of the current implementation. I've been working on improving performance, which has been going on quite good as far as I think. Basically I'm in the process of implementing similar optimisations that Bitcoin did for the last two years (but I'm alone with it) and planning on things Bitcoin doesn't even has yet. So please be patient.

Pruning will be a "continuous" progress. What I'm currently planning to do (at least as a first step) is to add RPC calls that can be executed manually and that will remove unnecessary information (like very old moves that are no longer needed since the current game state is known anyway) from disk. It won't change anything to the network-level protocol, and you will be the one to decide when and how often to do it. It won't be a hardfork or something that takes place at a certain time only.
To give more precise progress updates: It is already possible to prune the game state database (remove old game states), which brings game.dat down from 200 MiB to under 1 MiB. I'm already a good way towards pruning nameindexfull.dat (removing old name updates), which will (hopefully) remove almost all of the currently 1.8 GiB of nameindexfull.dat. After that, I'll try to work on the harder parts (blkindex.dat and eventually even the real chain on disk - this is something also Bitcoin doesn't have, AFAIK).