Jesus taught us to pray to God and scripture says we should not go to a mediator but instead go directly to Jesus Christ.
Jessu taught us to pray for others:
But I say to you, Love your enemies and pray for those who persecute you,Matthew 5:44
bless those who curse you, pray for those who abuse you.Luke 6:28
Saint Paul taught, by example, Christians to pray for others:
while they long for you and pray for you because of the surpassing grace of God that he has given you.2 Corinthians 9:14
For we rejoice when we are weak and you are strong. This is what we pray for, that you may become perfect.2 Corinthians 13:9
At the same time pray for us as well that God will open to us a door for the word, that we may declare the mystery of Christ, for which I am in prison,Colossians 4:3
Beloved, pray for us.1 Thessalonians 5:25
To this end we always pray for you, asking that our God will make you worthy of his call and will fulfil by his power every good resolve and work of faith,2 Thessalonians 1:11
Finally, brothers and sisters, pray for us, so that the word of the Lord may spread rapidly and be glorified everywhere, just as it is among you,2 Thessalonians 3:1
Pray for us; we are sure that we have a clear conscience, desiring to act honourably in all things.Hebrews 13:18
When we pray for one another, we mediate. It is an error to interpret 1 Timothy 2:5 in isolation from its context because its context is an exhortation to pray and to intercede for one another.
I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men; For kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty. For this is good and acceptable in the sight of God our Saviour; Who will have all men to be saved, and to come unto the knowledge of the truth. For there is one God, and one mediator between God and men, the man Christ Jesus; Who gave himself a ransom for all, to be testified in due time.
1 Timothy 2:1-6
Without its context your posts treat verse 5 as if it forbids intercession for others. As if having Christ as the only mediator who gave himself as a ransom for [the sins of] all, forbids Christians interceding for others, acting as mediators in prayer on behalf of others. The mediation of Christ, here in this passage, is that of the Saviour in his sacrifice for the sins of his people, and in this there can be no other mediator for no other sacrifice has been made for the sins of all. Yet the very same passage urgers that supplications, prayers, intercessions be made for all men, this is nothing less than to urge mediation in prayer for all men.