Now there are two ways in which man views good and bad. A man with the love of GOD views it different from that of an unbeliever. So those who are saved, feel concerned for everybody's salvation. This is the true nature of GOD. Because HE is love, he wants all men to be saved.
1. I don't see the relevance of how man views good and bad in regard to the topic of predestination?

2. You state how you think a saved man views "good and bad" but you made no mention of how you think an unsaved man views "good and bad"?
3. You have made an illogical jump from how a saved man views good and bad to feeling concerned for everybody's salvation. I don't see the connection?
4. Another totally illogical jump to go from a saved man is concerned for everybody's salvation to "this is the true nature of God." We can't deduce what God's nature is like from a fallen creature's emotive response to someone else, regardless if that person is saved or not. God's nature is only known from divine revelation, aka: the Bible.
(For this is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth. 1 Timothy 2:3-4)
So we cannot deny HIS sovereignty in salvation and also HE desires all men to be saved.
1. IF the 1Tim 2:3,4 actually teaches that God "desires" the salvation of all men, i.e., God "wills" that all men be saved, then de facto all men will infallibly be saved. For whatever God has determined to be will be since He is the sovereign Creator and Sustainer of all things Who governs His creation completely for His glory. Did you not read any of the Scripture passages I provided for you in my first reply that speak to this very issue? (Isa 44:7; 45:21; 46:9,10; Jer 32:19; Ps 33:11; 135:6; Dan 4:35; Rom 11:33-36; Eph 1:9-11)

2. It is more than important that we take biblical passages IN CONTEXT to rightly come to understand the truth they teach. In this particular case, re: 1Tim 2:3,4 this is especially true. Thus...
1 Timothy 2:1-4 (ASV) "I exhort therefore, first of all, that supplications, prayers, intercessions, thanksgivings, be made for all men; for kings and all that are in high place; that we may lead a tranquil and quiet life in all godliness and gravity. This is good and acceptable in the sight of God our Saviour; who would have all men to be saved, and come to the knowledge of the truth."
It can now be clearly seen that the "all men" that appears in verse 4 is the same "all men" that appears beforehand in verse 1. The "all men" refers to "kings and all that are in a high place", i.e., those who rule over others. Understandably, since in Paul's day and throughout history those in power have misused their power to oppress those under their rule, the natural tendency is to not pray for such evil individuals. But here Paul makes clear that even these types of people can be saved and so it is good to pray for them too... thus there is no TYPE or CLASS of individual which God hasn't desired to save. For a fuller exegetical treatment of this passage, see here:
An Exegetical Study of 1Timothy 2:4.
This is true love of GOD. So one thing is sure that HE doesn't prompt us to do evil.
Sorry, but I must admit that I do not understand how or where this statement fits in??
If both are true, then we are in a situation where we cannot for sure explain how election and
GOD'S desire to save all mankind go together.
There is no such alleged paradox. For, God does not love all men and God has not decreed (willed/desired) all men to be saved. Romans 9 has much to say about God's love, election, purpose in creating some to honor (salvation) and some to dishonor (damnation) as well as answering such objections to God's indisputable sovereignty, including salvation.
Also remember that one thing that remains forever is the perfect love of GOD.
(And now abide faith, hope, love, these three; but the greatest of these is love. 1 Corinthians 13:13).
Ooops! Once again, it is important to take a passage in context. 1Cor 13 is addressing OUR love, true love for others. Thus "love" appears in the triad, "faith, hope and love"... God doesn't have faith nor hope.

So,because GOD loves his creation, there should be freedom in our thoughts and actions.
Hmmmmm, this is another illogical leap. What is the correlation between God loving His creation and the necessity of there being freedom in a man's thoughts and actions?

Now the ultimate question is how free will exists? Remember that we may not know how GOD accomplishes these things. Such knowledge is a mystery and probably out of our understanding.
Our conception of time and space is different from that of GOD. So I think that all mankind
is given a fair chance of salvation. According to the scripture this is true. It is also
true that only some will be saved in the end.
But how these events go together is a mystery which we cannot know. It is better left to
GOD himself. That is the reason I think, GOD did not reveal these things to us.
1. The ultimate answer is: "Free will doesn't exist", thus all else that rests upon this presupposition is mute and not worth thinking about.

2. What is most incomprehensible is the relationship between God's sovereignty and man's responsibility. Scripture most definitely teaches both. Thus, they are embraced by faith rather than diminishing God's sovereignty by allocating some of His sovereignty to man and man's limited knowledge and power to God.
3. Could you please show from Scripture where this "all mankind is given a fair chance of salvation" idea is found? And could you please define/explain what this "fair chance of salvation" is?
4. Lastly, from this it would appear that man determines his own salvation by exercising his "free will" and God simply complies with man's decision... would this be an accurate summary of your view?
In His grace,