"Paradise" is often understood before the Resurrection as "Abraham's bosom" which was the place in Hades where the righteous went to wait.
Yes, Christ was there with the thief after they both died.
Abraham's Bosom is mentioned only one time in the bible from the parable that was given and if you are going to interpret the parable in a literal sense it means that there are people being tormented in flames even now.
Furthermore, the bible says that Jesus after he died was in the "heart of the earth"
Mat 12:40 For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth.
So is the heart of the earth the same paradise the same as "Abraham's Bosom?
Also the bible teaches that both the wicked and the righteous are in the graves until the resurrection.
Joh 5:28 Marvel not at this: for the hour is coming, in the which
all that are in the graves shall hear his voice,
Joh 5:29 And shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation.
Dan 12:1 And at that time shall Michael stand up, the great prince which standeth for the children of thy people: and there shall be a time of trouble, such as never was since there was a nation even to that same time: and at that time thy people shall be delivered, every one that shall be found written in the book.
Dan 12:2
And many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt.
Job 14:10 But man dieth, and wasteth away: yea, man giveth up the ghost, and where is he?
Job 14:11 As the waters fail from the sea, and the flood decayeth and drieth up:
Job 14:12
So man lieth down, and riseth not: till the heavens be no more, they shall not awake, nor be raised out of their sleep.
Job 14:13 O that thou wouldest hide me in the grave, that thou wouldest keep me secret, until thy wrath be past, that thou wouldest appoint me a set time, and remember me!
Job 14:14 If a man die, shall he live again? all the days of my appointed time will I wait, till my change come.
1Co 15:51 Behold, I shew you a mystery;
We shall not all sleep, but we shall all be changed,
1Co 15:52 In a moment, in the twinkling of an eye,
at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
1Co 15:53 For this corruptible must put on incorruption, and this mortal must put on immortality.
1Co 15:54 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written,
Death is swallowed up in victory.
1Co 15:55 O death, where is thy sting? O grave, where is thy victory?
In light of all these scriptures, lets look at the experience of Lazarus who was dead and resurrected. If indeed Lazarus went to heaven or paradise or Abraham's Bosom then why is there no record of him sharing his amazing post-death experience. Lazarus would have been the only person who was dead for so long and brought back to life. In fact, nobody else who was resurrected by Jesus shared any experience taken anywhere in another dimension, in another form or anything like that.