Why do Catholics have statues when the Bible forbids them?
The Bible does not forbid the making of statues, but the worship of statues. In Exodus 25:18, God commands the Israelites to make statues of the cherubim for the Ark of the Covenant. We don't worship statues. We simply use them as holy reminders when we pray.
Why do Catholics keep relics of the saints?
The relics of the saints are holy reminders of the bodily resurrection, which will happen on the last day. Also, in the Bible a dead man is resurrected when he touches the bones of Elisha (2 Kgs. 13:21) and the sick are healed by touching Paul's handkerchief (Acts 19:12). Jesus came to "make all things new" (Rev. 21:5). When the Son of God took on human flesh the spirit and flesh were reconciled to each other. Now we receive God's grace through material things — like when Jesus used clay to heal the blind man (cf. John 9:6). Just like that clay or Paul's handkerchief, the relics of the saints, in Christ, are also channels of grace.
Why do Catholics pray to the saints when the Bible forbids contacting dead spirits (cf. Deut. 18:11; 1 Sam. 28:6ff.)?
The Bible forbids necromancy or trying to obtain information from the dead which otherwise belongs to God alone, such as knowledge of the future. The saints, moreover, are not dead, but alive, for God "is not God of the dead, but of the living" (Luke 20:38). In fact, in Mark 9:4, Elijah and Moses appear to Jesus and have a conversation with Him.
Read more about the Saints in the Catechism of the Catholic Church.
Why do Catholics pray to the saints when Jesus is the "one mediator between God and men" (1 Tim. 2:5)?
When Paul calls Jesus our one Mediator he is referring to His sacrifice on the Cross. Because Jesus is both God and man, His death alone had the power to reconcile us with God. This is a mediation of sacrifice. The intercession of the saints, though, is a mediation of prayer, which is entirely different. Paul calls all Christians to this kind of mediation a few verses earlier, saying, "I ask that supplications, prayers, petitions, and thanksgivings be offered for everyone ... . This is good and pleasing to God our savior" (1 Tim. 2:1, 3).
Why do Catholics talk about the saints in heaven when the Bible calls believers on earth the saints?
"Saint" can refer to a believer on earth or a soul in heaven. In Colossians 1:12, Paul says the saints on earth "share in the inheritance of the holy ones in light." So we're saints with a small "s," meaning we're still in the process of being made perfect (cf. Phil. 2:12). Revelation 5:8 shows the twenty-four elders in heaven offering up to God the prayers of the saints on earth in the form of "gold bowls filled with incense."