Firstly, if I by Beelzebub cast out devils, is rhetorical. They accused Jesus of calling other forces into play rather than God - not having any belief in who Jesus really was. In other words, it's like saying, 'he who lives by the sword, will die by the sword'. Matt 26:52 By what you trust in, that will be your standard. (Just as he rebuked the Jews, saying, the devil was their father, they will be held to account under the law if they live by self, evil and lies instead of honouring God John 8:44)
Jesus came to deal with sin and death - he cannot do that under authority of Satan - hence the 'kingdom divided' spiel in v25, he does it under God's authority. Satan will never forgive anyone - if they appeal to him as a judge, they are dead already!
Apostles judging the twelve tribes of Israel and the saints will judge the world are the same thing in that they will be under Christ as chief judge - this authority given him by the Father.
And He (God) has given Him (Jesus) authority to execute judgment, because He is the Son of Man. John 5:27
The apostles/disciples are from Israel and have been appropriately chosen to judge their fellows. The saints (others and gentiles) will do similarly over the rest of humanity.
Jesus is the one true judge, who has earned the right to call all men to account and pass sentence - all guilty!
There is none more qualified to judge than one of our own. Jesus, as Timothy points out - is one of us.
1 Tim 2:5 For there is one God, and there is one mediator between God and men, the man Christ Jesus.
He (God) will judge the world in righteousness through a Man whom He has appointed, having furnished proof to all men by raising Him from the dead. Acts 17:31
The model of being an agent for judgement is shown in Exodus 18:22 where Moses found he was overwhelmed with judging the people all day … God told him to get organised and prepare others to do this work with him - not for him - as they are all working for God - just as Jesus is under God's authority, working for Him.
Exodus 18:13 And it came to pass on the morrow, that Moses sat to judge the people: and the people stood by Moses from the morning unto the evening.
And let them judge the people at all seasons: and it shall be, that every great matter they shall bring unto thee, but every small matter they shall judge: so shall it be easier for thyself, and they shall bear the burden with thee.
The role of Jesus' judgement is not to condemn, but to bring to salvation. He warned to not judge one another,
1 “Do not judge so that you will not be judged. 2 “For in the way you judge, you will be judged; and by your standard of measure, it will be measured to you. Matt 7:1-2
Jesus is the only way to salvation, but first, each must be brought to account of their total failure at 'being good' - then, through the repentant heart that God provides, they may finally accept Jesus' sacrifice to cover their sins too. Judging is under the law of life and grace, OR the old law of sin and death.
If one does not recognise God's authority in Jesus (as the Pharisees did not), they reject God and are left with the hard result of sin - death!
If one refuses grace, through Jesus' sacrifice, the law still stands and eternal death awaits.
Of course, believers (in theory - sheep and goats aside) are already judged and have been included in Christ as saved and await their rebirth into the kingdom when Jesus returns.