By Jonathan Spicer and Ahmed RasheedANKARA/BAGHDAD, May 13 (Reuters) - Just two weeks after Turkey's parliament made recommendations on how to advance the country's peace process with Kurdish militants, the Iran war broke out, plunging the Middle East into fresh instability and bringing new doubts on both sides.Turkey has warned of the risk of new Kurdish mobilisations in Iran and Iraq and, according to a government official, played a key role in quashing a short-lived U.S.-Israeli idea to back...