“Did the Old Testament and kingdom saints (future ones also) have assurance of salvation and how does it compare with the assurance we have in the dispensation of grace?”

It will be easier for me to attach a study of salvation in the OT and concept of salvation in the Kingdom program which will help your understanding.

When you read this you should see the answer to your question.  But let me add to this by saying:  No one possessed eternal life in their soul until the Holy Spirit came.  Then the Kingdom Saint was “born again” of the Spirit of God.  John 1:11-13 says it this way:

“He came unto his own, and his own received him not.  But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:  Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.” 

Jesus Christ came and was rejected in His earthly ministry, up to and including the cross.

He gave them power to become the sons of God when He poured out the Holy Spirit in Acts 2.

It is then, for the first time, Believers possessed eternal life in their soul.  Before that it was the promise of eternal life.

Now then, according to  I John 2:18-20…25-27;  the Holy Spirit will secure them – even through the future time we call the tribulation.

“Little children, it is the last time: and as ye have heard that antichrist shall come, even now are there many antichrists; whereby we know that it is the last time.  They went out from us, but they were not of us; for if they had been of us, they would no doubt have continued with us: but they went out, that they might be made manifest that they were not all of us.  But ye have an unction from the Holy One, and ye know all things…… And this is the promise that he hath promised us, even eternal life.  These things have I written unto you concerning them that seduce you.  But the anointing which ye have received of him abideth in you, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in him.”

Hope this much helps.  If you cannot bring in the attachment, let me know and I will send it as an email.