How GoldMint are going to solve these issues?

The Nothing-at-Stake and LongRange-Attack issues are well known. Just like 51% attack in PoW algorithm.

Earlier, GoldMint commented on the PoS issues in a blog post here — https://blog.goldmint.io/goldmint-blockchain-why-custom-85e339756253.

The Nothing-at-Stake issue is the event of a fork (the “fork” can be a malicious attempt to rewrite the history and do a double spend) the optimal strategy for any validator is to validate every chain, so that the validator gets their reward no matter which fork wins. This means that consensus algorithm doesn’t work as intended.

The attacker may be able to send a transaction to an exchange for some digital commodity (usually another cryptocurrency), receive the commodity and then start a fork of the blockchain from one block behind the transaction and send the money to themselves instead.

Even with 1% of the total stake the attacker’s fork would win because everyone else is mining on both.

There is no single PoS algorithm that can suit everyone. Because of that GoldMint has chosen the path of building its own highly specialized blockchain instead of building an all-purpose solution. Currently our engineers are designing the blockchain while keeping Nothing-at-stake problem in mind.

There are different approaches to handle the matter. Ethereum Casper uses so called “slashing conditions”: in case the validator is cheating and the conditions are met, he loses his deposit. Graphene doesn’t use deposits, but the cheating witness (validator) can be excluded from the list of active witnesses.

Please also notice that “statistical simulations have shown that simultaneous forging on several chains is possible, even profitable. But Proof-of-Stake advocates believe most described attack scenarios are impossible or so unpredictable that they are only theoretical” (https://en.wikipedia.org/wiki/Proof-of-stake).