Taking your last first, there were may unbelievers present when Lazarus was raised up:What do you think about the idea that the signs you've cited were only to be witnessed by believers, or sincere seekers, because our Lord said,
An evil and adulterous generation seeketh after a sign; and there shall no sign be given to it, but the sign of the prophet Jonas Mt.12:39
It seems they were asking from doubt. I'm not sure if anyone who doubted like that ever saw Jesus do a miracle.
42 "And I know that You always hear Me, but because of the people who are standing by I said this, that they may believe that You sent Me."
43 Now when He had said these things, He cried with a loud voice, "Lazarus, come forth!"
44 And he who had died came out bound hand and foot with graveclothes, and his face was wrapped with a cloth. Jesus said to them, "Loose him, and let him go."
45 Then many of the Jews who had come to Mary, and had seen the things Jesus did, believed in Him.
46 But some of them went away to the Pharisees and told them the things Jesus did.
47 Then the chief priests and the Pharisees gathered a council and said, "What shall we do? For this Man works many signs.
48 "If we let Him alone like this, everyone will believe in Him, and the Romans will come and take away both our place and nation."
(Jn. 11:42-48 NKJ)
What do you think about the idea that the signs you've cited were only to be witnessed by believers, or sincere seekers, because our Lord said,
An evil and adulterous generation seeketh after a sign; and there shall no sign be given to it, but the sign of the prophet Jonas Mt.12:39
Contradicting that theory, Christ implored unbelievers to believe BECAUSE of the miracles He did:
37 "If I do not do the works of My Father, do not believe Me;
38 "but if I do, though you do not believe Me, believe the works, that you may know and believe that the Father is in Me, and I in Him (Jn. 10:37-38 NKJ)
Christ said an evil and adulterous generation seeks a sign, because they were being evil and adulterous, refusing to believe the signs they saw. They insisted on more, not because they wanted proof but because they were looking for ways to accuse Him:
9 Now when He had departed from there, He went into their synagogue.
10 And behold, there was a man who had a withered hand. And they asked Him, saying, "Is it lawful to heal on the Sabbath?"-- that they might accuse Him.
11 Then He said to them, "What man is there among you who has one sheep, and if it falls into a pit on the Sabbath, will not lay hold of it and lift it out?
12 "Of how much more value then is a man than a sheep? Therefore it is lawful to do good on the Sabbath."
13 Then He said to the man, "Stretch out your hand." And he stretched it out, and it was restored as whole as the other.
14 Then the Pharisees went out and plotted against Him, how they might destroy Him. (Matt. 12:9-14 NKJ)