When Jesus talked to the two disciples of the scriptures how did they react?

Their hearts burned when Jesus expounded on the scriptures to them.

Source:

Luke 24:32

Which of the Apostles specifically acknowledged Paul’s writings as scripture?

Peter acknowledged Paul’s writings as scripture in his Second Epistle.

Source: 2^nd Peter 3:15

Paul especially wanted Timothy to bring this when he met him at Rome. What did Paul want?

His parchments possibly his papers also his notes on Bible study,

Source:

^nd Timothy 4:13

Paul told this person to study to show himself approved. Who is he writing to?

Paul told Timothy to “Study to shew thyself approved unto God…” In his 2^nd letter to Timothy.

Source: 2^nd Timothy 2:15

God commanded the study of the law through Moses. Where in the house did he command them to write the law?

God commanded them to write the law on their doorposts. To this day Jews do this with small container called a Mezuzoth also spelled Mezuzah.

Source:

Deuteronomy 6:10 and others