What happens when there is a warrant for arrest?

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I am the victim of a crime. The perpetrator failed to appear in court and I have been informed that a warrant has been issued for his arrest.

Can anyone help me please to understand what this means in practical terms? If he doesn't voluntarily hand himself in will the police go looking for him? If they do go to his house, will they arrest him on the spot or just ask him to attend a station? Or are they just going to write to him and hope he turns himself in? I don't know the man well but I believe he is possibly mentally impaired/special needs; would this affect it at all?

Second question: the police were trying to rush the case to court as it was nearing the time limit for the statute of limitations. Now that he hasn't appeared but the process has been started, has the clock stopped and there's no need to worry, or will the case be thrown out if he doesn't appear in court before the end of the original time period?

Thanks for any help. I have a witness care officer but it is difficult to get hold of him.

An arrest warrant means the police have the powers to arrest the defendant, detain him and produce him in court. What they will actually do is up to them.

There is no need to worry about time limits. The time is from the offence being committed until the courts are notified of the charge. The courts have clearly been notified, so there is no longer any rush. The defendant cannot escape the charge by simply going into hiding.