Does God still require believers under grace not to partake of these things?
Yes, God still demands that even under grace believers do not partake of these things, because the life of the flesh is in the blood and because God explicitly forbids immoral sins that believers must have nothing to do with.
Les explains from Leviticus 17 that the life of the flesh is in the blood, and that is why blood had to be sacrificed for the remission of sin—death for life. The blood had to be applied, sprinkled on the altar, the Ark of the Covenant, and the Mercy Seat, and Christ also had to present His blood in heaven. For this reason, Les teaches, God still demands that even under grace we do not partake of these things. He also notes the second point: believers are not to practice fornication or immorality. In Leviticus 18 God explicitly lays down immoral sins that believers are to have nothing to do with, not following the doings of the land of Egypt.
Does God still expect believers under grace to abstain from blood?
Yes. God still demands that even under grace, believers do not partake of blood. The life of the flesh is in the blood, and blood was given on the altar to make atonement for souls. Therefore, the requirement to abstain from blood continues for believers under grace.
Does God still hold believers accountable for abstaining from idols, blood, strangled things, and fornication even though they are under grace?
Yes. Even though believers are under Grace and not under Law, God still holds them accountable to abstain from meat offered to idols, blood, things strangled, and fornication. This requirement was part of the written agreement from Jerusalem, and keeping yourselves from these things means you shall do well.