You have asked two questions which have two different answers.  Let’s look at them separately and then see if we can understand them together.

We read in Genesis 18:14, “Is any thing too hard for the LORD?”  Of course this a rhetorical question showing that there is nothing too hard for the Lord to do.  He cannot be defeated.  His purpose cannot be thwarted.  There is no problem that He cannot solve.  However, is there anything that is impossible to God?  Yes, there are some things that the Lord cannot do.  At first, that answer might shock or offend you.  There are some things that the very nature of God does not allow Him to do and the Bible clearly tells us this.  For example, it is impossible for God to tell a lie!  Titus 1:2says, “In hope of eternal life, which God, that cannot lie, promised before the world began.”  I’m sure you will agree with that.

It is impossible for God to change!  Malachi 3:6 says, “For I am the LORD, I change not.”  Remember, the Lord cannot lie, so when He tells us that He does not change, we can know that for a fact.  For the Lord to change would mean that He could become better.  He is already perfect, so we see that He cannot change.  God cannot be tempted to sin.  James 1:13 says, “Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man.”  As a believer on the Lord Jesus Christ, the Lord cannot abandon you.  In Hebrews 13:5 the Lord tells us, “I will never leave thee, nor forsake thee.”  There are more scriptures we could look at, but I think that is enough to convince us that the Lord cannot do anything that is contrary to His perfect nature.

Can God do anything He wants to do?  Absolutely, yes He can.  We read in 2 Samuel 22:31, “As for God, his way is perfect…”  Psalm 115:3 states it emphatically, “But our God is in the heavens: he hath done whatsoever he hath pleased.”  Yes, God can do anything He wants to do.  It is His essential pure and holy nature that assures us that God does not want to do some things, but all He wants to do, He can…and will.  Can God sin?  NO!  Does God want to sin?  NO!  Well, what if God changes His mind?  He can’t because His will is perfect and He changes not.

Is there anything the Lord wants, but does not get?  Sadly, yes.  1 Timothy 2:4 tells us that the Lord “…Who will have all men to be saved, and to come unto the knowledge of the truth.”  The Lord wants everyone to be saved.  He loves you and sent His Son to die on the cross to pay your sin debt.  He wants you to believe on the Lord Jesus Christ and be saved.  In Ezekiel 33:11, the Lord says, “I have no pleasure in the death of the wicked; but that the wicked turn from his way and live.  If you have not put your faith in the Lord Jesus Christ, I urge you to bow your knee before Him now and accept His free gift of salvation.  Romans 10:9 says, “That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.”  (208.2)