A few comments from a non-expert:
- Is it correct to name the state as Jerusalem, Kingdom without mentioning a real ruler? As this type was struck in the name of the Islamic ruler it seems inappropriate to attribute it to one of the kings of Jerusalem.
- Why there was a need to make an imitation? They were a trade coinage intended for use in Syria, where the moslems would presumably be resistant to coins with the cross on them.
- Why coin was minted in Christian state in the name of Arabic ruler? See previous answer
- Who was al-Salih Isma'il? (Perhaps, this guy: As-Salih Ismail al-Malik - Wikipedia ?) No,
As-Salih Ismail - Wikipedia,_Emir_of_Damascus
- Where may I find and copy from Arabic texts from the obverse and reverse with translations? Sorry I can't help with this, but our member Maythem may be able to help
- Are catalog references correct? Yes, Metcalf quotes the Bates numbers and the Metcalf numbers refer to later issues without readable mints or dates. I'm afraid I don't have my copy of Malloy here to check the CCS number though. The date for this should be c.1253-1260 not 1244. The mint is uncertain: they could have been minted at Acre or Tripoli
- How big is the diameter? They vary so I'm afraid you'd have to ask the owner this.
[edit] I forgot to say that Metcalf calls these 'imitative dracmas' rather than dirhems.
I hope this helps.
Alan