Iphone5 can I put my sim in it straight away?

Found an iphone5, took it to the police then unclaimed so was returned to myself, now the question is, I put it to factory restore after taking out the Vodafone sim and want to put another sim in…(my own three mobile), I do realise I need a nano sim card
but will that be OK or is there anything I need to do first.
I put a cut down card (o2, the one that says to activate phone 248) to see if it would work, it searches and finds o2 but I can't call anyone as its like no signal. It all opens so can't be locked, gives the time, date, footsie all up to date so any help appreciated. Don't want to phone a company and they think its stolen… Yes just thought I should have asked for a receipt from the police, to late now had it for 3weeks.

1. Is the cut down sim card activated already?
2. Is the iphone factory unlocked?
3. Might be blacklisted

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